Method and apparatus for video coding

ABSTRACT

Aspects of the disclosure provide a method and an apparatus including processing circuitry for video decoding. The processing circuitry decodes coded information for a transform block (TB) from a coded video bitstream. The coded information indicates one of intra prediction mode information that indicates an intra prediction mode used for the TB, a size of the TB, and a primary transform type used for the TB. The processing circuitry determines a context for entropy decoding a secondary transform index based on the one of the intra prediction mode information for the TB, the size of the TB, and the primary transform type used for the TB. The secondary transform index indicates a secondary transform in a set of secondary transforms that is to be performed on the TB. The processing circuitry entropy decodes the secondary transform index based on the context and performs the secondary transform.

INCORPORATION BY REFERENCE

This present disclosure claims the benefit of priority to U.S.Provisional Application No. 63/112,529, “CONTEXT DESIGN FOR ENTROPYCODING OF SECONDARY TRANSFORM INDEX” filed on Nov. 11, 2020, which isincorporated by reference herein in its entirety.

TECHNICAL FIELD

The present disclosure describes embodiments generally related to videocoding.

BACKGROUND

The background description provided herein is for the purpose ofgenerally presenting the context of the disclosure. Work of thepresently named inventors, to the extent the work is described in thisbackground section, as well as aspects of the description that may nototherwise qualify as prior art at the time of filing, are neitherexpressly nor impliedly admitted as prior art against the presentdisclosure.

Video coding and decoding can be performed using inter-pictureprediction with motion compensation. Uncompressed digital video caninclude a series of pictures, each picture having a spatial dimensionof, for example, 1920×1080 luminance samples and associated chrominancesamples. The series of pictures can have a fixed or variable picturerate (informally also known as frame rate), of, for example 60 picturesper second or 60 Hz. Uncompressed video has specific bitraterequirements. For example, 1080p60 4:2:0 video at 8 bit per sample(1920×1080 luminance sample resolution at 60 Hz frame rate) requiresclose to 1.5 Gbit/s bandwidth. An hour of such video requires more than600 GBytes of storage space.

One purpose of video coding and decoding can be the reduction ofredundancy in the input video signal, through compression. Compressioncan help reduce the aforementioned bandwidth and/or storage spacerequirements, in some cases by two orders of magnitude or more. Bothlossless compression and lossy compression, as well as a combinationthereof can be employed. Lossless compression refers to techniques wherean exact copy of the original signal can be reconstructed from thecompressed original signal. When using lossy compression, thereconstructed signal may not be identical to the original signal, butthe distortion between original and reconstructed signals is smallenough to make the reconstructed signal useful for the intendedapplication. In the case of video, lossy compression is widely employed.The amount of distortion tolerated depends on the application; forexample, users of certain consumer streaming applications may toleratehigher distortion than users of television distribution applications.The compression ratio achievable can reflect that: higherallowable/tolerable distortion can yield higher compression ratios.

A video encoder and decoder can utilize techniques from several broadcategories, including, for example, motion compensation, transform,quantization, and entropy coding.

Video codec technologies can include techniques known as intra coding.In intra coding, sample values are represented without reference tosamples or other data from previously reconstructed reference pictures.In some video codecs, the picture is spatially subdivided into blocks ofsamples. When all blocks of samples are coded in intra mode, thatpicture can be an intra picture. Intra pictures and their derivationssuch as independent decoder refresh pictures, can be used to reset thedecoder state and can, therefore, be used as the first picture in acoded video bitstream and a video session, or as a still image. Thesamples of an intra block can be exposed to a transform, and thetransform coefficients can be quantized before entropy coding. Intraprediction can be a technique that minimizes sample values in thepre-transform domain. In some cases, the smaller the DC value after atransform is, and the smaller the AC coefficients are, the fewer thebits that are required at a given quantization step size to representthe block after entropy coding.

Traditional intra coding such as known from, for example MPEG-2generation coding technologies, does not use intra prediction. However,some newer video compression technologies include techniques thatattempt, from, for example, surrounding sample data and/or metadataobtained during the encoding and/or decoding of spatially neighboring,and preceding in decoding order, blocks of data. Such techniques arehenceforth called “intra prediction” techniques. Note that in at leastsome cases, intra prediction is using reference data only from thecurrent picture under reconstruction and not from reference pictures.

There can be many different forms of intra prediction. When more thanone of such techniques can be used in a given video coding technology,the technique in use can be coded in an intra prediction mode. Incertain cases, modes can have submodes and/or parameters, and those canbe coded individually or included in the mode codeword. Which codewordto use for a given mode, submode, and/or parameter combination can havean impact in the coding efficiency gain through intra prediction, and socan the entropy coding technology used to translate the codewords into abitstream.

A certain mode of intra prediction was introduced with H.264, refined inH.265, and further refined in newer coding technologies such as jointexploration model (JEM), versatile video coding (VVC), and benchmark set(BMS). A predictor block can be formed using neighboring sample valuesbelonging to already available samples. Sample values of neighboringsamples are copied into the predictor block according to a direction. Areference to the direction in use can be coded in the bitstream or mayitself be predicted.

Referring to FIG. 1A, depicted in the lower right is a subset of ninepredictor directions known from H.265's 33 possible predictor directions(corresponding to the 33 angular modes of the 35 intra modes). The pointwhere the arrows converge (101) represents the sample being predicted.The arrows represent the direction from which the sample is beingpredicted. For example, arrow (102) indicates that sample (101) ispredicted from a sample or samples to the upper right, at a 45 degreeangle from the horizontal. Similarly, arrow (103) indicates that sample(101) is predicted from a sample or samples to the lower left of sample(101), in a 22.5 degree angle from the horizontal.

Still referring to FIG. 1A, on the top left there is depicted a squareblock (104) of 4×4 samples (indicated by a dashed, boldface line). Thesquare block (104) includes 16 samples, each labelled with an “S”, itsposition in the Y dimension (e.g., row index) and its position in the Xdimension (e.g., column index). For example, sample S21 is the secondsample in the Y dimension (from the top) and the first (from the left)sample in the X dimension. Similarly, sample S44 is the fourth sample inblock (104) in both the Y and X dimensions. As the block is 4×4 samplesin size, S44 is at the bottom right. Further shown are reference samplesthat follow a similar numbering scheme. A reference sample is labelledwith an R, its Y position (e.g., row index) and X position (columnindex) relative to block (104). In both H.264 and H.265, predictionsamples neighbor the block under reconstruction; therefore no negativevalues need to be used.

Intra picture prediction can work by copying reference sample valuesfrom the neighboring samples as appropriated by the signaled predictiondirection. For example, assume the coded video bitstream includessignaling that, for this block, indicates a prediction directionconsistent with arrow (102)—that is, samples are predicted from aprediction sample or samples to the upper right, at a 45 degree anglefrom the horizontal. In that case, samples S41, S32, S23, and S14 arepredicted from the same reference sample R05. Sample S44 is thenpredicted from reference sample R08.

In certain cases, the values of multiple reference samples may becombined, for example through interpolation, in order to calculate areference sample; especially when the directions are not evenlydivisible by 45 degrees.

The number of possible directions has increased as video codingtechnology has developed. In H.264 (year 2003), nine different directioncould be represented. That increased to 33 in H.265 (year 2013), andJEM/VVC/BMS, at the time of disclosure, can support up to 65 directions.Experiments have been conducted to identify the most likely directions,and certain techniques in the entropy coding are used to represent thoselikely directions in a small number of bits, accepting a certain penaltyfor less likely directions. Further, the directions themselves cansometimes be predicted from neighboring directions used in neighboring,already decoded, blocks.

FIG. 1B shows a schematic (180) that depicts 65 intra predictiondirections according to JEM to illustrate the increasing number ofprediction directions over time.

The mapping of intra prediction directions bits in the coded videobitstream that represent the direction can be different from videocoding technology to video coding technology; and can range, forexample, from simple direct mappings of prediction direction to intraprediction mode, to codewords, to complex adaptive schemes involvingmost probable modes, and similar techniques. In all cases, however,there can be certain directions that are statistically less likely tooccur in video content than certain other directions. As the goal ofvideo compression is the reduction of redundancy, those less likelydirections will, in a well working video coding technology, berepresented by a larger number of bits than more likely directions.

Motion compensation can be a lossy compression technique and can relateto techniques where a block of sample data from a previouslyreconstructed picture or part thereof (reference picture), after beingspatially shifted in a direction indicated by a motion vector (MVhenceforth), is used for the prediction of a newly reconstructed pictureor picture part. In some cases, the reference picture can be the same asthe picture currently under reconstruction. MVs can have two dimensionsX and Y, or three dimensions, the third being an indication of thereference picture in use (the latter, indirectly, can be a timedimension).

In some video compression techniques, an MV applicable to a certain areaof sample data can be predicted from other MVs, for example from thoserelated to another area of sample data spatially adjacent to the areaunder reconstruction, and preceding that MV in decoding order. Doing socan substantially reduce the amount of data required for coding the MV,thereby removing redundancy and increasing compression. MV predictioncan work effectively, for example, because when coding an input videosignal derived from a camera (known as natural video) there is astatistical likelihood that areas larger than the area to which a singleMV is applicable move in a similar direction and, therefore, can in somecases be predicted using a similar motion vector derived from MVs ofneighboring area. That results in the MV found for a given area to besimilar or the same as the MV predicted from the surrounding MVs, andthat in turn can be represented, after entropy coding, in a smallernumber of bits than what would be used if coding the MV directly. Insome cases, MV prediction can be an example of lossless compression of asignal (namely: the MVs) derived from the original signal (namely: thesample stream). In other cases, MV prediction itself can be lossy, forexample because of rounding errors when calculating a predictor fromseveral surrounding MVs.

Various MV prediction mechanisms are described in H.265/HEVC (ITU-T Rec.H.265, “High Efficiency Video Coding”, December 2016). Out of the manyMV prediction mechanisms that H.265 offers, described here is atechnique henceforth referred to as “spatial merge”.

Referring to FIG. 2, a current block (201) comprises samples that havebeen found by the encoder during the motion search process to bepredictable from a previous block of the same size that has beenspatially shifted. Instead of coding that MV directly, the MV can bederived from metadata associated with one or more reference pictures,for example from the most recent (in decoding order) reference picture,using the MV associated with either one of five surrounding samples,denoted A0, A1, and B0, B1, B2 (202 through 206, respectively). InH.265, the MV prediction can use predictors from the same referencepicture that the neighboring block is using.

SUMMARY

Aspects of the disclosure provide methods and apparatuses for videoencoding and/or decoding. In some examples, an apparatus for videodecoding includes processing circuitry. The processing circuitry candecode coded information for a transform block (TB) from a coded videobitstream. The coded information can indicate one of intra predictionmode information for the TB, a size of the TB, and a primary transformtype used for the TB. The intra prediction mode information for the TBcan indicate an intra prediction mode used for the TB. The processingcircuitry can determine a context for entropy decoding a secondarytransform index based on the one of the intra prediction modeinformation for the TB, the size of the TB, and the primary transformtype used for the TB. The secondary transform index can indicate asecondary transform in a set of secondary transforms that is to beperformed on the TB. The processing circuitry can entropy decode thesecondary transform index based on the context and perform the secondarytransform indicated by the secondary transform index on the TB.

In an embodiment, the one of the intra prediction mode information forthe TB, the size of the TB, and the primary transform type used for theTB can indicate the size of the TB. The processing circuitry candetermine the context for entropy decoding the secondary transform indexbased on the size of the TB. In an example, the size of the TB indicatesa width W of the TB and a height H of the TB, a minimum of the width Wof the TB and the height H of the TB is L, and the processing circuitrycan determine the context based on L or L×L.

In an embodiment, the one of the intra prediction mode information forthe TB, the size of the TB, and the primary transform type used for theTB can indicate the intra prediction mode information for the TB. Theprocessing circuitry can determine the context for entropy decoding thesecondary transform index based on the intra prediction mode informationfor the TB.

In an example, the intra prediction mode information for the TBindicates a nominal mode index, the TB being predicted using adirectional prediction mode that is determined based on the nominal modeindex and an angular offset, and the processing circuitry can determinethe context for entropy decoding the secondary transform index based onthe nominal mode index.

In an example, the intra prediction mode information for the TBindicates a nominal mode index. The TB can be predicted using adirectional prediction mode that is determined based on the nominal modeindex and an angular offset. The processing circuitry can determine thecontext for entropy decoding the secondary transform index based on anindex value associated with the nominal mode index.

In an example, the intra prediction mode information for the TBindicates a non-directional prediction mode index. The TB can bepredicted using a non-directional prediction mode indicated by thenon-directional prediction mode index. The processing circuitry candetermine the context for entropy decoding the secondary transform indexbased on the non-directional prediction mode index.

In an example, the intra prediction mode information for the TBindicates a recursive filtering mode used to predict the TB. Theprocessing circuitry can determine a nominal mode index based on therecursive filtering mode. The nominal mode index can indicate a nominalmode. The processing circuitry can determine the context for entropydecoding the secondary transform index based on the nominal mode index.

In an embodiment, the one of the intra prediction mode information forthe TB, the size of the TB, and the primary transform type used for theTB can indicate the primary transform type used for the TB. Theprocessing circuitry can determine the context for entropy decoding thesecondary transform index based on the primary transform type used forthe TB.

A primary transform indicated by the primary transform type can includea horizontal transform indicated by a horizontal primary transform typeand a vertical transform indicated by a vertical primary transform type.In an example, the processing circuitry determines the context forentropy decoding the secondary transform index based on whether thehorizontal primary transform type and the vertical primary transformtype are both discrete cosine transforms (DCTs) or both asymmetricdiscrete sine transforms (ADSTs).

In an example, the processing circuitry determines the context forentropy decoding the secondary transform index based on whether thehorizontal primary transform type and the vertical primary transformtype are both discrete cosine transforms (DCTs) or both line graphtransforms (LGTs).

In an example, the processing circuitry determines the context forentropy decoding the secondary transform index based on whether thehorizontal primary transform type and the vertical primary transformtype are (i) both discrete cosine transforms (DCTs), (ii) both linegraph transforms (LGTs), (iii) a DCT and an LGT, respectively, or (iv)an LGT and a DCT, respectively.

In an example, the processing circuitry determines the context forentropy decoding the secondary transform index based on whether thehorizontal primary transform type and the vertical primary transformtype are (i) both discrete cosine transforms (DCTs), (ii) both linegraph transforms (LGTs), (iii) a DCT and an identity transform (IDTX),respectively, or (iv) an IDTX and a DCT, respectively.

Aspects of the disclosure also provide non-transitory computer-readablemediums storing instructions which when executed by a computer for videodecoding cause the computer to perform the methods for video decodingand/or encoding.

BRIEF DESCRIPTION OF THE DRAWINGS

Further features, the nature, and various advantages of the disclosedsubject matter will be more apparent from the following detaileddescription and the accompanying drawings in which:

FIG. 1A is a schematic illustration of an exemplary subset of intraprediction modes.

FIG. 1B is an illustration of exemplary intra prediction directions.

FIG. 2 is a schematic illustration of a current block and itssurrounding spatial merge candidates in one example.

FIG. 3 is a schematic illustration of a simplified block diagram of acommunication system (300) in accordance with an embodiment.

FIG. 4 is a schematic illustration of a simplified block diagram of acommunication system (400) in accordance with an embodiment.

FIG. 5 is a schematic illustration of a simplified block diagram of adecoder in accordance with an embodiment.

FIG. 6 is a schematic illustration of a simplified block diagram of anencoder in accordance with an embodiment.

FIG. 7 shows a block diagram of an encoder in accordance with anotherembodiment.

FIG. 8 shows a block diagram of a decoder in accordance with anotherembodiment.

FIG. 9 shows an example of nominal modes for a coding block according toan embodiment of the disclosure.

FIG. 10 shows examples for non-directional smooth intra predictionaccording to aspects of the disclosure.

FIG. 11 shows an example of a recursive-filtering-based intra predictoraccording to an embodiment of the disclosure.

FIG. 12 shows an example of multiple reference lines for a coding blockaccording to an embodiment of the disclosure.

FIG. 13 shows an example of transform block partition on a blockaccording to an embodiment of the disclosure.

FIG. 14 shows an example of transform block partition on a blockaccording to an embodiment of the disclosure.

FIG. 15 shows examples of primary transform basis functions according toembodiments of the disclosure.

FIG. 16A shows exemplary dependencies of availability of varioustransform kernels based on a transform block size and a prediction modeaccording to embodiments of the disclosure.

FIG. 16B shows exemplary transform type selections based on an intraprediction mode according to embodiments of the disclosure.

FIG. 16C shows an example of a generic line graph transform (LGT)characterized by self-loop weights and edge weights according to anembodiment of the disclosure.

FIG. 16D shows an exemplary generalized graph Laplacian (GGL) matrixaccording to an embodiment of the disclosure.

FIGS. 17-18 show examples of two transform coding processes (1700) and(1800) using a 16×64 transform and a 16×48 transform, respectivelyaccording to embodiments of the disclosure.

FIG. 19 shows a flow chart outlining a process (1900) according to anembodiment of the disclosure.

FIG. 20 is a schematic illustration of a computer system in accordancewith an embodiment.

DETAILED DESCRIPTION OF EMBODIMENTS

FIG. 3 illustrates a simplified block diagram of a communication system(300) according to an embodiment of the present disclosure. Thecommunication system (300) includes a plurality of terminal devices thatcan communicate with each other, via, for example, a network (350). Forexample, the communication system (300) includes a first pair ofterminal devices (310) and (320) interconnected via the network (350).In the FIG. 3 example, the first pair of terminal devices (310) and(320) performs unidirectional transmission of data. For example, theterminal device (310) may code video data (e.g., a stream of videopictures that are captured by the terminal device (310)) fortransmission to the other terminal device (320) via the network (350).The encoded video data can be transmitted in the form of one or morecoded video bitstreams. The terminal device (320) may receive the codedvideo data from the network (350), decode the coded video data torecover the video pictures and display video pictures according to therecovered video data. Unidirectional data transmission may be common inmedia serving applications and the like.

In another example, the communication system (300) includes a secondpair of terminal devices (330) and (340) that performs bidirectionaltransmission of coded video data that may occur, for example, duringvideoconferencing. For bidirectional transmission of data, in anexample, each terminal device of the terminal devices (330) and (340)may code video data (e.g., a stream of video pictures that are capturedby the terminal device) for transmission to the other terminal device ofthe terminal devices (330) and (340) via the network (350). Eachterminal device of the terminal devices (330) and (340) also may receivethe coded video data transmitted by the other terminal device of theterminal devices (330) and (340), and may decode the coded video data torecover the video pictures and may display video pictures at anaccessible display device according to the recovered video data.

In the FIG. 3 example, the terminal devices (310), (320), (330) and(340) may be illustrated as servers, personal computers and smart phonesbut the principles of the present disclosure may be not so limited.Embodiments of the present disclosure find application with laptopcomputers, tablet computers, media players and/or dedicated videoconferencing equipment. The network (350) represents any number ofnetworks that convey coded video data among the terminal devices (310),(320), (330) and (340), including for example wireline (wired) and/orwireless communication networks. The communication network (350) mayexchange data in circuit-switched and/or packet-switched channels.Representative networks include telecommunications networks, local areanetworks, wide area networks and/or the Internet. For the purposes ofthe present discussion, the architecture and topology of the network(350) may be immaterial to the operation of the present disclosureunless explained herein below.

FIG. 4 illustrates, as an example for an application for the disclosedsubject matter, the placement of a video encoder and a video decoder ina streaming environment. The disclosed subject matter can be equallyapplicable to other video enabled applications, including, for example,video conferencing, digital TV, storing of compressed video on digitalmedia including CD, DVD, memory stick and the like, and so on.

A streaming system may include a capture subsystem (413), that caninclude a video source (401), for example a digital camera, creating forexample a stream of video pictures (402) that are uncompressed. In anexample, the stream of video pictures (402) includes samples that aretaken by the digital camera. The stream of video pictures (402),depicted as a bold line to emphasize a high data volume when compared toencoded video data (404) (or coded video bitstreams), can be processedby an electronic device (420) that includes a video encoder (403)coupled to the video source (401). The video encoder (403) can includehardware, software, or a combination thereof to enable or implementaspects of the disclosed subject matter as described in more detailbelow. The encoded video data (404) (or encoded video bitstream (404)),depicted as a thin line to emphasize the lower data volume when comparedto the stream of video pictures (402), can be stored on a streamingserver (405) for future use. One or more streaming client subsystems,such as client subsystems (406) and (408) in FIG. 4 can access thestreaming server (405) to retrieve copies (407) and (409) of the encodedvideo data (404). A client subsystem (406) can include a video decoder(410), for example, in an electronic device (430). The video decoder(410) decodes the incoming copy (407) of the encoded video data andcreates an outgoing stream of video pictures (411) that can be renderedon a display (412) (e.g., display screen) or other rendering device (notdepicted). In some streaming systems, the encoded video data (404),(407), and (409) (e.g., video bitstreams) can be encoded according tocertain video coding/compression standards. Examples of those standardsinclude ITU-T Recommendation H.265. In an example, a video codingstandard under development is informally known as Versatile Video Coding(VVC). The disclosed subject matter may be used in the context of VVC.

It is noted that the electronic devices (420) and (430) can includeother components (not shown). For example, the electronic device (420)can include a video decoder (not shown) and the electronic device (430)can include a video encoder (not shown) as well.

FIG. 5 shows a block diagram of a video decoder (510) according to anembodiment of the present disclosure. The video decoder (510) can beincluded in an electronic device (530). The electronic device (530) caninclude a receiver (531) (e.g., receiving circuitry). The video decoder(510) can be used in the place of the video decoder (410) in the FIG. 4example.

The receiver (531) may receive one or more coded video sequences to bedecoded by the video decoder (510); in the same or another embodiment,one coded video sequence at a time, where the decoding of each codedvideo sequence is independent from other coded video sequences. Thecoded video sequence may be received from a channel (501), which may bea hardware/software link to a storage device which stores the encodedvideo data. The receiver (531) may receive the encoded video data withother data, for example, coded audio data and/or ancillary data streams,that may be forwarded to their respective using entities (not depicted).The receiver (531) may separate the coded video sequence from the otherdata. To combat network jitter, a buffer memory (515) may be coupled inbetween the receiver (531) and an entropy decoder/parser (520) (“parser(520)” henceforth). In certain applications, the buffer memory (515) ispart of the video decoder (510). In others, it can be outside of thevideo decoder (510) (not depicted). In still others, there can be abuffer memory (not depicted) outside of the video decoder (510), forexample to combat network jitter, and in addition another buffer memory(515) inside the video decoder (510), for example to handle playouttiming. When the receiver (531) is receiving data from a store/forwarddevice of sufficient bandwidth and controllability, or from anisosynchronous network, the buffer memory (515) may not be needed, orcan be small. For use on best effort packet networks such as theInternet, the buffer memory (515) may be required, can be comparativelylarge and can be advantageously of adaptive size, and may at leastpartially be implemented in an operating system or similar elements (notdepicted) outside of the video decoder (510).

The video decoder (510) may include the parser (520) to reconstructsymbols (521) from the coded video sequence. Categories of those symbolsinclude information used to manage operation of the video decoder (510),and potentially information to control a rendering device such as arender device (512) (e.g., a display screen) that is not an integralpart of the electronic device (530) but can be coupled to the electronicdevice (530), as was shown in FIG. 5. The control information for therendering device(s) may be in the form of Supplemental EnhancementInformation (SEI messages) or Video Usability Information (VUI)parameter set fragments (not depicted). The parser (520) mayparse/entropy-decode the coded video sequence that is received. Thecoding of the coded video sequence can be in accordance with a videocoding technology or standard, and can follow various principles,including variable length coding, Huffman coding, arithmetic coding withor without context sensitivity, and so forth. The parser (520) mayextract from the coded video sequence, a set of subgroup parameters forat least one of the subgroups of pixels in the video decoder, based uponat least one parameter corresponding to the group. Subgroups can includeGroups of Pictures (GOPs), pictures, tiles, slices, macroblocks, CodingUnits (CUs), blocks, Transform Units (TUs), Prediction Units (PUs) andso forth. The parser (520) may also extract from the coded videosequence information such as transform coefficients, quantizer parametervalues, motion vectors, and so forth.

The parser (520) may perform an entropy decoding/parsing operation onthe video sequence received from the buffer memory (515), so as tocreate symbols (521).

Reconstruction of the symbols (521) can involve multiple different unitsdepending on the type of the coded video picture or parts thereof (suchas: inter and intra picture, inter and intra block), and other factors.Which units are involved, and how, can be controlled by the subgroupcontrol information that was parsed from the coded video sequence by theparser (520). The flow of such subgroup control information between theparser (520) and the multiple units below is not depicted for clarity.

Beyond the functional blocks already mentioned, the video decoder (510)can be conceptually subdivided into a number of functional units asdescribed below. In a practical implementation operating undercommercial constraints, many of these units interact closely with eachother and can, at least partly, be integrated into each other. However,for the purpose of describing the disclosed subject matter, theconceptual subdivision into the functional units below is appropriate.

A first unit is the scaler/inverse transform unit (551). Thescaler/inverse transform unit (551) receives a quantized transformcoefficient as well as control information, including which transform touse, block size, quantization factor, quantization scaling matrices,etc. as symbol(s) (521) from the parser (520). The scaler/inversetransform unit (551) can output blocks comprising sample values, thatcan be input into aggregator (555).

In some cases, the output samples of the scaler/inverse transform (551)can pertain to an intra coded block; that is: a block that is not usingpredictive information from previously reconstructed pictures, but canuse predictive information from previously reconstructed parts of thecurrent picture. Such predictive information can be provided by an intrapicture prediction unit (552). In some cases, the intra pictureprediction unit (552) generates a block of the same size and shape ofthe block under reconstruction, using surrounding already reconstructedinformation fetched from the current picture buffer (558). The currentpicture buffer (558) buffers, for example, partly reconstructed currentpicture and/or fully reconstructed current picture. The aggregator(555), in some cases, adds, on a per sample basis, the predictioninformation the intra prediction unit (552) has generated to the outputsample information as provided by the scaler/inverse transform unit(551).

In other cases, the output samples of the scaler/inverse transform unit(551) can pertain to an inter coded, and potentially motion compensatedblock. In such a case, a motion compensation prediction unit (553) canaccess reference picture memory (557) to fetch samples used forprediction. After motion compensating the fetched samples in accordancewith the symbols (521) pertaining to the block, these samples can beadded by the aggregator (555) to the output of the scaler/inversetransform unit (551) (in this case called the residual samples orresidual signal) so as to generate output sample information. Theaddresses within the reference picture memory (557) from where themotion compensation prediction unit (553) fetches prediction samples canbe controlled by motion vectors, available to the motion compensationprediction unit (553) in the form of symbols (521) that can have, forexample X, Y, and reference picture components. Motion compensation alsocan include interpolation of sample values as fetched from the referencepicture memory (557) when sub-sample exact motion vectors are in use,motion vector prediction mechanisms, and so forth.

The output samples of the aggregator (555) can be subject to variousloop filtering techniques in the loop filter unit (556). Videocompression technologies can include in-loop filter technologies thatare controlled by parameters included in the coded video sequence (alsoreferred to as coded video bitstream) and made available to the loopfilter unit (556) as symbols (521) from the parser (520), but can alsobe responsive to meta-information obtained during the decoding ofprevious (in decoding order) parts of the coded picture or coded videosequence, as well as responsive to previously reconstructed andloop-filtered sample values.

The output of the loop filter unit (556) can be a sample stream that canbe output to the render device (512) as well as stored in the referencepicture memory (557) for use in future inter-picture prediction.

Certain coded pictures, once fully reconstructed, can be used asreference pictures for future prediction. For example, once a codedpicture corresponding to a current picture is fully reconstructed andthe coded picture has been identified as a reference picture (by, forexample, the parser (520)), the current picture buffer (558) can becomea part of the reference picture memory (557), and a fresh currentpicture buffer can be reallocated before commencing the reconstructionof the following coded picture.

The video decoder (510) may perform decoding operations according to apredetermined video compression technology in a standard, such as ITU-TRec. H.265. The coded video sequence may conform to a syntax specifiedby the video compression technology or standard being used, in the sensethat the coded video sequence adheres to both the syntax of the videocompression technology or standard and the profiles as documented in thevideo compression technology or standard. Specifically, a profile canselect certain tools as the only tools available for use under thatprofile from all the tools available in the video compression technologyor standard. Also necessary for compliance can be that the complexity ofthe coded video sequence is within bounds as defined by the level of thevideo compression technology or standard. In some cases, levels restrictthe maximum picture size, maximum frame rate, maximum reconstructionsample rate (measured in, for example megasamples per second), maximumreference picture size, and so on. Limits set by levels can, in somecases, be further restricted through Hypothetical Reference Decoder(HRD) specifications and metadata for HRD buffer management signaled inthe coded video sequence.

In an embodiment, the receiver (531) may receive additional (redundant)data with the encoded video. The additional data may be included as partof the coded video sequence(s). The additional data may be used by thevideo decoder (510) to properly decode the data and/or to moreaccurately reconstruct the original video data. Additional data can bein the form of, for example, temporal, spatial, or signal noise ratio(SNR) enhancement layers, redundant slices, redundant pictures, forwarderror correction codes, and so on.

FIG. 6 shows a block diagram of a video encoder (603) according to anembodiment of the present disclosure. The video encoder (603) isincluded in an electronic device (620). The electronic device (620)includes a transmitter (640) (e.g., transmitting circuitry). The videoencoder (603) can be used in the place of the video encoder (403) in theFIG. 4 example.

The video encoder (603) may receive video samples from a video source(601) (that is not part of the electronic device (620) in the FIG. 6example) that may capture video image(s) to be coded by the videoencoder (603). In another example, the video source (601) is a part ofthe electronic device (620).

The video source (601) may provide the source video sequence to be codedby the video encoder (603) in the form of a digital video sample streamthat can be of any suitable bit depth (for example: 8 bit, 10 bit, 12bit, . . . ), any colorspace (for example, BT.601 Y CrCB, RGB, . . . ),and any suitable sampling structure (for example Y CrCb 4:2:0, Y CrCb4:4:4). In a media serving system, the video source (601) may be astorage device storing previously prepared video. In a videoconferencingsystem, the video source (601) may be a camera that captures local imageinformation as a video sequence. Video data may be provided as aplurality of individual pictures that impart motion when viewed insequence. The pictures themselves may be organized as a spatial array ofpixels, wherein each pixel can comprise one or more samples depending onthe sampling structure, color space, etc. in use. A person skilled inthe art can readily understand the relationship between pixels andsamples. The description below focuses on samples.

According to an embodiment, the video encoder (603) may code andcompress the pictures of the source video sequence into a coded videosequence (643) in real time or under any other time constraints asrequired by the application. Enforcing appropriate coding speed is onefunction of a controller (650). In some embodiments, the controller(650) controls other functional units as described below and isfunctionally coupled to the other functional units. The coupling is notdepicted for clarity. Parameters set by the controller (650) can includerate control related parameters (picture skip, quantizer, lambda valueof rate-distortion optimization techniques, . . . ), picture size, groupof pictures (GOP) layout, maximum motion vector search range, and soforth. The controller (650) can be configured to have other suitablefunctions that pertain to the video encoder (603) optimized for acertain system design.

In some embodiments, the video encoder (603) is configured to operate ina coding loop. As an oversimplified description, in an example, thecoding loop can include a source coder (630) (e.g., responsible forcreating symbols, such as a symbol stream, based on an input picture tobe coded, and a reference picture(s)), and a (local) decoder (633)embedded in the video encoder (603). The decoder (633) reconstructs thesymbols to create the sample data in a similar manner as a (remote)decoder also would create (as any compression between symbols and codedvideo bitstream is lossless in the video compression technologiesconsidered in the disclosed subject matter). The reconstructed samplestream (sample data) is input to the reference picture memory (634). Asthe decoding of a symbol stream leads to bit-exact results independentof decoder location (local or remote), the content in the referencepicture memory (634) is also bit exact between the local encoder andremote encoder. In other words, the prediction part of an encoder “sees”as reference picture samples exactly the same sample values as a decoderwould “see” when using prediction during decoding. This fundamentalprinciple of reference picture synchronicity (and resulting drift, ifsynchronicity cannot be maintained, for example because of channelerrors) is used in some related arts as well.

The operation of the “local” decoder (633) can be the same as of a“remote” decoder, such as the video decoder (510), which has alreadybeen described in detail above in conjunction with FIG. 5. Brieflyreferring also to FIG. 5, however, as symbols are available andencoding/decoding of symbols to a coded video sequence by an entropycoder (645) and the parser (520) can be lossless, the entropy decodingparts of the video decoder (510), including the buffer memory (515), andparser (520) may not be fully implemented in the local decoder (633).

An observation that can be made at this point is that any decodertechnology except the parsing/entropy decoding that is present in adecoder also necessarily needs to be present, in substantially identicalfunctional form, in a corresponding encoder. For this reason, thedisclosed subject matter focuses on decoder operation. The descriptionof encoder technologies can be abbreviated as they are the inverse ofthe comprehensively described decoder technologies. Only in certainareas a more detail description is required and provided below.

During operation, in some examples, the source coder (630) may performmotion compensated predictive coding, which codes an input picturepredictively with reference to one or more previously coded picture fromthe video sequence that were designated as “reference pictures.” In thismanner, the coding engine (632) codes differences between pixel blocksof an input picture and pixel blocks of reference picture(s) that may beselected as prediction reference(s) to the input picture.

The local video decoder (633) may decode coded video data of picturesthat may be designated as reference pictures, based on symbols createdby the source coder (630). Operations of the coding engine (632) mayadvantageously be lossy processes. When the coded video data may bedecoded at a video decoder (not shown in FIG. 6), the reconstructedvideo sequence typically may be a replica of the source video sequencewith some errors. The local video decoder (633) replicates decodingprocesses that may be performed by the video decoder on referencepictures and may cause reconstructed reference pictures to be stored inthe reference picture cache (634). In this manner, the video encoder(603) may store copies of reconstructed reference pictures locally thathave common content as the reconstructed reference pictures that will beobtained by a far-end video decoder (absent transmission errors).

The predictor (635) may perform prediction searches for the codingengine (632). That is, for a new picture to be coded, the predictor(635) may search the reference picture memory (634) for sample data (ascandidate reference pixel blocks) or certain metadata such as referencepicture motion vectors, block shapes, and so on, that may serve as anappropriate prediction reference for the new pictures. The predictor(635) may operate on a sample block-by-pixel block basis to findappropriate prediction references. In some cases, as determined bysearch results obtained by the predictor (635), an input picture mayhave prediction references drawn from multiple reference pictures storedin the reference picture memory (634).

The controller (650) may manage coding operations of the source coder(630), including, for example, setting of parameters and subgroupparameters used for encoding the video data.

Output of all aforementioned functional units may be subjected toentropy coding in the entropy coder (645). The entropy coder (645)translates the symbols as generated by the various functional units intoa coded video sequence, by lossless compressing the symbols according totechnologies such as Huffman coding, variable length coding, arithmeticcoding, and so forth.

The transmitter (640) may buffer the coded video sequence(s) as createdby the entropy coder (645) to prepare for transmission via acommunication channel (660), which may be a hardware/software link to astorage device which would store the encoded video data. The transmitter(640) may merge coded video data from the video coder (603) with otherdata to be transmitted, for example, coded audio data and/or ancillarydata streams (sources not shown).

The controller (650) may manage operation of the video encoder (603).During coding, the controller (650) may assign to each coded picture acertain coded picture type, which may affect the coding techniques thatmay be applied to the respective picture. For example, pictures oftenmay be assigned as one of the following picture types:

An Intra Picture (I picture) may be one that may be coded and decodedwithout using any other picture in the sequence as a source ofprediction. Some video codecs allow for different types of intrapictures, including, for example Independent Decoder Refresh (“IDR”)Pictures. A person skilled in the art is aware of those variants of Ipictures and their respective applications and features.

A predictive picture (P picture) may be one that may be coded anddecoded using intra prediction or inter prediction using at most onemotion vector and reference index to predict the sample values of eachblock.

A bi-directionally predictive picture (B Picture) may be one that may becoded and decoded using intra prediction or inter prediction using atmost two motion vectors and reference indices to predict the samplevalues of each block. Similarly, multiple-predictive pictures can usemore than two reference pictures and associated metadata for thereconstruction of a single block.

Source pictures commonly may be subdivided spatially into a plurality ofsample blocks (for example, blocks of 4×4, 8×8, 4×8, or 16×16 sampleseach) and coded on a block-by-block basis. Blocks may be codedpredictively with reference to other (already coded) blocks asdetermined by the coding assignment applied to the blocks' respectivepictures. For example, blocks of I pictures may be codednon-predictively or they may be coded predictively with reference toalready coded blocks of the same picture (spatial prediction or intraprediction). Pixel blocks of P pictures may be coded predictively, viaspatial prediction or via temporal prediction with reference to onepreviously coded reference picture. Blocks of B pictures may be codedpredictively, via spatial prediction or via temporal prediction withreference to one or two previously coded reference pictures.

The video encoder (603) may perform coding operations according to apredetermined video coding technology or standard, such as ITU-T Rec.H.265. In its operation, the video encoder (603) may perform variouscompression operations, including predictive coding operations thatexploit temporal and spatial redundancies in the input video sequence.The coded video data, therefore, may conform to a syntax specified bythe video coding technology or standard being used.

In an embodiment, the transmitter (640) may transmit additional datawith the encoded video. The source coder (630) may include such data aspart of the coded video sequence. Additional data may comprisetemporal/spatial/SNR enhancement layers, other forms of redundant datasuch as redundant pictures and slices, SEI messages, VUI parameter setfragments, and so on.

A video may be captured as a plurality of source pictures (videopictures) in a temporal sequence. Intra-picture prediction (oftenabbreviated to intra prediction) makes use of spatial correlation in agiven picture, and inter-picture prediction makes uses of the (temporalor other) correlation between the pictures. In an example, a specificpicture under encoding/decoding, which is referred to as a currentpicture, is partitioned into blocks. When a block in the current pictureis similar to a reference block in a previously coded and still bufferedreference picture in the video, the block in the current picture can becoded by a vector that is referred to as a motion vector. The motionvector points to the reference block in the reference picture, and canhave a third dimension identifying the reference picture, in casemultiple reference pictures are in use.

In some embodiments, a bi-prediction technique can be used in theinter-picture prediction. According to the bi-prediction technique, tworeference pictures, such as a first reference picture and a secondreference picture that are both prior in decoding order to the currentpicture in the video (but may be in the past and future, respectively,in display order) are used. A block in the current picture can be codedby a first motion vector that points to a first reference block in thefirst reference picture, and a second motion vector that points to asecond reference block in the second reference picture. The block can bepredicted by a combination of the first reference block and the secondreference block.

Further, a merge mode technique can be used in the inter-pictureprediction to improve coding efficiency.

According to some embodiments of the disclosure, predictions, such asinter-picture predictions and intra-picture predictions are performed inthe unit of blocks. For example, according to the HEVC standard, apicture in a sequence of video pictures is partitioned into coding treeunits (CTU) for compression, the CTUs in a picture have the same size,such as 64×64 pixels, 32×32 pixels, or 16×16 pixels. In general, a CTUincludes three coding tree blocks (CTBs), which are one luma CTB and twochroma CTBs. Each CTU can be recursively quadtree split into one ormultiple coding units (CUs). For example, a CTU of 64×64 pixels can besplit into one CU of 64×64 pixels, or 4 CUs of 32×32 pixels, or 16 CUsof 16×16 pixels. In an example, each CU is analyzed to determine aprediction type for the CU, such as an inter prediction type or an intraprediction type. The CU is split into one or more prediction units (PUs)depending on the temporal and/or spatial predictability. Generally, eachPU includes a luma prediction block (PB), and two chroma PBs. In anembodiment, a prediction operation in coding (encoding/decoding) isperformed in the unit of a prediction block. Using a luma predictionblock as an example of a prediction block, the prediction block includesa matrix of values (e.g., luma values) for pixels, such as 8×8 pixels,16×16 pixels, 8×16 pixels, 16×8 pixels, and the like.

FIG. 7 shows a diagram of a video encoder (703) according to anotherembodiment of the disclosure. The video encoder (703) is configured toreceive a processing block (e.g., a prediction block) of sample valueswithin a current video picture in a sequence of video pictures, andencode the processing block into a coded picture that is part of a codedvideo sequence. In an example, the video encoder (703) is used in theplace of the video encoder (403) in the FIG. 4 example.

In an HEVC example, the video encoder (703) receives a matrix of samplevalues for a processing block, such as a prediction block of 8×8samples, and the like. The video encoder (703) determines whether theprocessing block is best coded using intra mode, inter mode, orbi-prediction mode using, for example, rate-distortion optimization.When the processing block is to be coded in intra mode, the videoencoder (703) may use an intra prediction technique to encode theprocessing block into the coded picture; and when the processing blockis to be coded in inter mode or bi-prediction mode, the video encoder(703) may use an inter prediction or bi-prediction technique,respectively, to encode the processing block into the coded picture. Incertain video coding technologies, merge mode can be an inter pictureprediction submode where the motion vector is derived from one or moremotion vector predictors without the benefit of a coded motion vectorcomponent outside the predictors. In certain other video codingtechnologies, a motion vector component applicable to the subject blockmay be present. In an example, the video encoder (703) includes othercomponents, such as a mode decision module (not shown) to determine themode of the processing blocks.

In the FIG. 7 example, the video encoder (703) includes the interencoder (730), an intra encoder (722), a residue calculator (723), aswitch (726), a residue encoder (724), a general controller (721), andan entropy encoder (725) coupled together as shown in FIG. 7.

The inter encoder (730) is configured to receive the samples of thecurrent block (e.g., a processing block), compare the block to one ormore reference blocks in reference pictures (e.g., blocks in previouspictures and later pictures), generate inter prediction information(e.g., description of redundant information according to inter encodingtechnique, motion vectors, merge mode information), and calculate interprediction results (e.g., predicted block) based on the inter predictioninformation using any suitable technique. In some examples, thereference pictures are decoded reference pictures that are decoded basedon the encoded video information.

The intra encoder (722) is configured to receive the samples of thecurrent block (e.g., a processing block), in some cases compare theblock to blocks already coded in the same picture, generate quantizedcoefficients after transform, and in some cases also intra predictioninformation (e.g., an intra prediction direction information accordingto one or more intra encoding techniques). In an example, the intraencoder (722) also calculates intra prediction results (e.g., predictedblock) based on the intra prediction information and reference blocks inthe same picture.

The general controller (721) is configured to determine general controldata and control other components of the video encoder (703) based onthe general control data. In an example, the general controller (721)determines the mode of the block, and provides a control signal to theswitch (726) based on the mode. For example, when the mode is the intramode, the general controller (721) controls the switch (726) to selectthe intra mode result for use by the residue calculator (723), andcontrols the entropy encoder (725) to select the intra predictioninformation and include the intra prediction information in thebitstream; and when the mode is the inter mode, the general controller(721) controls the switch (726) to select the inter prediction resultfor use by the residue calculator (723), and controls the entropyencoder (725) to select the inter prediction information and include theinter prediction information in the bitstream.

The residue calculator (723) is configured to calculate a difference(residue data) between the received block and prediction resultsselected from the intra encoder (722) or the inter encoder (730). Theresidue encoder (724) is configured to operate based on the residue datato encode the residue data to generate the transform coefficients. In anexample, the residue encoder (724) is configured to convert the residuedata from a spatial domain to a frequency domain, and generate thetransform coefficients. The transform coefficients are then subject toquantization processing to obtain quantized transform coefficients. Invarious embodiments, the video encoder (703) also includes a residuedecoder (728). The residue decoder (728) is configured to performinverse-transform, and generate the decoded residue data. The decodedresidue data can be suitably used by the intra encoder (722) and theinter encoder (730). For example, the inter encoder (730) can generatedecoded blocks based on the decoded residue data and inter predictioninformation, and the intra encoder (722) can generate decoded blocksbased on the decoded residue data and the intra prediction information.The decoded blocks are suitably processed to generate decoded picturesand the decoded pictures can be buffered in a memory circuit (not shown)and used as reference pictures in some examples.

The entropy encoder (725) is configured to format the bitstream toinclude the encoded block. The entropy encoder (725) is configured toinclude various information according to a suitable standard, such asthe HEVC standard. In an example, the entropy encoder (725) isconfigured to include the general control data, the selected predictioninformation (e.g., intra prediction information or inter predictioninformation), the residue information, and other suitable information inthe bitstream. Note that, according to the disclosed subject matter,when coding a block in the merge submode of either inter mode orbi-prediction mode, there is no residue information.

FIG. 8 shows a diagram of a video decoder (810) according to anotherembodiment of the disclosure. The video decoder (810) is configured toreceive coded pictures that are part of a coded video sequence, anddecode the coded pictures to generate reconstructed pictures. In anexample, the video decoder (810) is used in the place of the videodecoder (410) in the FIG. 4 example.

In the FIG. 8 example, the video decoder (810) includes an entropydecoder (871), an inter decoder (880), a residue decoder (873), areconstruction module (874), and an intra decoder (872) coupled togetheras shown in FIG. 8.

The entropy decoder (871) can be configured to reconstruct, from thecoded picture, certain symbols that represent the syntax elements ofwhich the coded picture is made up. Such symbols can include, forexample, the mode in which a block is coded (such as, for example, intramode, inter mode, bi-predicted mode, the latter two in merge submode oranother submode), prediction information (such as, for example, intraprediction information or inter prediction information) that canidentify certain sample or metadata that is used for prediction by theintra decoder (872) or the inter decoder (880), respectively, residualinformation in the form of, for example, quantized transformcoefficients, and the like. In an example, when the prediction mode isinter or bi-predicted mode, the inter prediction information is providedto the inter decoder (880); and when the prediction type is the intraprediction type, the intra prediction information is provided to theintra decoder (872). The residual information can be subject to inversequantization and is provided to the residue decoder (873).

The inter decoder (880) is configured to receive the inter predictioninformation, and generate inter prediction results based on the interprediction information.

The intra decoder (872) is configured to receive the intra predictioninformation, and generate prediction results based on the intraprediction information.

The residue decoder (873) is configured to perform inverse quantizationto extract de-quantized transform coefficients, and process thede-quantized transform coefficients to convert the residual from thefrequency domain to the spatial domain. The residue decoder (873) mayalso require certain control information (to include the QuantizerParameter (QP)), and that information may be provided by the entropydecoder (871) (data path not depicted as this may be low volume controlinformation only).

The reconstruction module (874) is configured to combine, in the spatialdomain, the residual as output by the residue decoder (873) and theprediction results (as output by the inter or intra prediction modulesas the case may be) to form a reconstructed block, that may be part ofthe reconstructed picture, which in turn may be part of thereconstructed video. It is noted that other suitable operations, such asa deblocking operation and the like, can be performed to improve thevisual quality.

It is noted that the video encoders (403), (603), and (703), and thevideo decoders (410), (510), and (810) can be implemented using anysuitable technique. In an embodiment, the video encoders (403), (603),and (703), and the video decoders (410), (510), and (810) can beimplemented using one or more integrated circuits. In anotherembodiment, the video encoders (403), (603), and (603), and the videodecoders (410), (510), and (810) can be implemented using one or moreprocessors that execute software instructions.

Video coding technologies related to context design for entropy codingof an index such as a secondary transform index are disclosed. The indexcan be used to identify one among a set of non-separable secondarytransforms used for coding (e.g., encoding and/or decoding) a block. Thecontext design for entropy coding of the index can be applicable in anysuitable video coding format or standard. The video coding format caninclude an open video coding format designed for video transmissionsover the Internet, such as AOMedia Video 1 (AV1) or a next generationAOMedia Video format beyond the AV1. The video coding standard caninclude High Efficiency Video Coding (HEVC) standard, a next-generationvideo coding beyond HEVC (e.g., the Versatile Video Coding (VVC)), orthe like.

Various intra prediction modes can be used in intra prediction, forexample, in AV1, VVC, and/or the like. In an embodiment, such as in theAV1, directional intra prediction is used. In the directional intraprediction, predicted samples for a block can be generated byextrapolating from neighboring reconstructed samples along a direction.The direction corresponds to an angle. A mode used in the directionalintra prediction to predict the predicted samples for the block can bereferred to as a directional mode (also referred to as directionalprediction modes, directional intra modes, directional intra predictionmodes, angular modes). Each directional mode can correspond to adifferent angle or a different direction. In an example, such as in anopen video coding format VP9, eight directional modes corresponding toeight angles from 45° to 207°, as shown in FIG. 9. The eight directionalmodes can also be referred to as nominal modes (e.g., V_PRED, H_PRED,D45_PRED, D135_PRED, D113_PRED, D157_PRED, D203_PRED, and D67_PRED). Toexploit more varieties of spatial redundancy in directional textures,for example in the AV1, directional modes can be extended, for example,beyond the eight nominal modes to an angular set with finer granularityand more angles (or directions), as shown in FIG. 9.

FIG. 9 shows an example of nominal modes for a coding block (CB) (910)according to an embodiment of the disclosure. Certain angles (referredto as nominal angles) can correspond to nominal modes. In an example,eight nominal angles (or nominal intra angles) (901)-(908) correspond tothe eight nominal modes (e.g., V_PRED, H_PRED, D45_PRED, D135_PRED,D113_PRED, D157_PRED, D203_PRED, and D67_PRED), respectively. The eightnominal angles (901)-(908) as well as the eight nominal modes can bereferred to as V_PRED, H_PRED, D45_PRED, D135_PRED, D113_PRED,D157_PRED, D203_PRED, and D67_PRED, respectively. A nominal mode indexcan indicate a nominal mode (e.g., one of the eight nominal modes). Inan example, the nominal mode index is signaled.

Further, each nominal angle can correspond to a plurality of finerangles (e.g., seven finer angles), and thus 56 angles (or predictionangles) or 56 directional modes (or angular modes, directional intraprediction modes) can be used, for example, in the AV1. Each predictionangle can be presented by a nominal angle and an angular offset (or anangle delta). The angular offset can be obtained by multiplying anoffset integer I (e.g., −3, −2, −1, 0, 1, 2, or 3) with a step size(e.g., 3°). In an example, the prediction angle is equal to a sum of thenominal angle and the angular offset. In an example, such as in the AV1,the nominal modes (e.g., the eight nominal modes (901)-(908)) togetherwith certain non-angular smooth modes (e.g., five non-angular smoothmodes such as a DC mode, a PAETH mode, a SMOOTH mode, a vertical SMOOTHmode, and a horizontal SMOOTH mode as described below) can be signaled.Subsequently, if a current prediction mode is a directional mode (or anangular mode), an index can be further signaled to indicate the angularoffset (e.g., the offset integer I) corresponding to the nominal angle.In an example, the directional mode (e.g., one of the 56 directionalmodes) can be determined based on the nominal mode index and the indexindicating the angular offset from the nominal mode. In an example, toimplement directional prediction modes via a generic way, the 56directional modes such as used in the AV1 are implemented with a unifieddirectional predictor that can project each pixel to a referencesub-pixel location and interpolate the reference pixel by a 2-tapbilinear filter.

Non-directional smooth intra predictors (also referred to asnon-directional smooth intra prediction modes, non-directional smoothmodes, non-angular smooth modes) can be used in intra prediction for ablock, such as a CB. In some examples (e.g., in the AV1), fivenon-directional smooth intra prediction modes include the DC mode or theDC predictor (e.g., DC), the PAETH mode or the PAETH predictor (e.g.,PAETH), the SMOOTH mode or the SMOOTH predictor (e.g., SMOOTH), thevertical SMOOTH mode (referred to as the SMOOTH_V mode, the SMOOTH_Vpredictor, the SMOOTH_V), and the horizontal SMOOTH mode (referred to asthe SMOOTH_H mode, the SMOOTH_H predictor, or SMOOTH_H).

FIG. 10 shows examples for non-directional smooth intra prediction modes(e.g., the DC mode, the PAETH mode, the SMOOTH mode, the SMOOTH_V mode,and the SMOOTH_H mode) according to aspects of the disclosure. Topredict a sample (1001) in a CB (1000) based on the DC predictor, anaverage of a first value of a left neighboring sample (1012) and asecond value of an above neighboring sample (or a top neighboringsample) (1011) can be used as a predictor.

To predict the sample (1001) based on the PAETH predictor, the firstvalue of the left neighboring sample (1012), the second value of the topneighboring sample (1011), and a third value for a top-left neighboringsample (1013) can be obtained. Then, a reference value is obtained usingEq. 1.

reference value=first value+second value−third value  (Eq. 1)

One of the first value, the second value, and the third value that isclosest to the reference value can be set as the predictor for thesample (1001).

The SMOOTH_V mode, the SMOOTH_H mode, and the SMOOTH mode can predictthe CB (1000) using a quadratic interpolation in a vertical direction, ahorizontal direction, and an average of the vertical direction and thehorizontal direction, respectively. To predict the sample (1001) basedon the SMOOTH predictor, an average (e.g., a weighted combination) ofthe first value, the second value, a value of a right sample (1014), anda value of a bottom sample (1016) can be used. In various examples, theright sample (1014) and the bottom sample (1016) are not reconstructed,and thus, a value of a top-right neighboring sample (1015) and a valueof a bottom-left neighboring sample (1017) can replace the values of theright sample (1014) and the bottom sample (1016), respectively.Accordingly, an average (e.g., a weighted combination) of the firstvalue, the second value, the value of the top-right neighboring sample(1015), and the value of the bottom-left neighboring sample (1017) canbe used as the SMOOTH predictor. To predict the sample (1001) based onthe SMOOTH_V predictor, an average (e.g., a weighted combination) of thesecond value of the top neighboring sample (1011) and the value of thebottom-left neighboring sample (1017) can be used. To predict the sample(1001) based on the SMOOTH_H predictor, an average (e.g., a weightedcombination) of the first value of the left neighboring sample (1012)and the value of the top-right neighboring sample (1015) can be used.

FIG. 11 shows an example of a recursive-filtering-based intra predictor(also referred to as a filter intra mode, or a recursive filtering mode)according to an embodiment of the disclosure. To capture a decayingspatial correlation with references on the edges, a filter intra modecan be used for a block, such as a CB (1100). In an example, the CB(1100) is a luma block. The luma block (1100) can be divided intomultiple patches (e.g., eight 4×2 patches B0-B7). Each of the patchesB0-B7 can have a plurality of neighboring samples. For example, thepatch B0 has seven neighboring samples (or seven neighbors) R00-R06including four top neighboring samples R01-R04, two left neighboringsamples R05-R06, and a top-left neighboring sample R00. Similarly, thepatch B7 has seven neighboring samples R70-R76 including four topneighboring samples R71-R74, two left neighboring samples R75-R76, and atop-left neighboring sample R70.

In some examples, multiple (e.g., five) filter intra modes (or multiplerecursive filtering modes) are pre-designed, for example, for the AV1.Each filter intra mode can be represented by a set of eight 7-tapfilters reflecting correlation between samples (or pixels) in acorresponding 4×2 patch (e.g., B0) and seven neighbors (e.g., R00-R06)that are adjacent to the 4×2 patch B0. Weighting factors for the 7-tapfilter can be position dependent. For each of the patches B0-B7, theseven neighbors (e.g., R00-R06 for B0, R70-R76 for B7) can be used topredict the samples in the corresponding patch. In an example, theneighbors R00-R06 are used to predict the samples in the patch B0. In anexample, the neighbors R70-R76 are used to predict the samples in thepatch B7. For certain patches in the CB (1100), such as the patch B0,all the seven neighbors (e.g., R00-R06) are already reconstructed. Forother patches in the CB (1100), at least one of the seven neighbors isnot reconstructed, and thus predicted value(s) of immediate neighbor(s)(or prediction sample(s) of immediate neighbor(s)) can be used asreference(s). For example, the seven neighbors R70-R76 of the patch B7are not reconstructed, so the prediction samples of the immediateneighbors can be used.

A chroma sample can be predicted from a luma sample. In an embodiment, achroma from luma mode (e.g., a CfL mode, a CfL predictor) is achroma-only intra predictor that can model chroma samples (or pixels) asa linear function of coincident reconstructed luma samples (or pixels).For example, the CfL prediction can be expressed using Eq. 2 as below.

CfL(α)=αL ^(A) +D  (Eq. 2)

where L^(A) denotes an AC contribution of a luma component, a denotes ascaling parameter of the linear model, and D denotes a DC contributionof a chroma component. In an example, reconstructed luma pixels aresubsampled based on a chroma resolution, and an average value issubtracted to form the AC contribution (e.g., L^(A)). To approximate achroma AC component from the AC contribution, instead of requiring adecoder to calculate the scaling parameter a, in some examples, such asin the AV1, the CfL mode determines the scaling parameter a based onoriginal chroma pixels and signals the scaling parameter a in abitstream, thus reducing decoder complexity and yielding a more preciseprediction. The DC contribution of the chroma component can be computedusing an intra DC mode. The intra DC mode can be sufficient for mostchroma content and have mature fast implementations.

Multi-line intra prediction can use more reference lines for intraprediction. A reference line can include multiple samples in a picture.In an example, the reference line includes samples in a row and samplesin a column. In an example, an encoder can determine and signal areference line used to generate the intra predictor. An index (alsoreferred to as a reference line index) indicating the reference line canbe signaled before intra prediction mode(s). In an example, only theMPMs are allowed when a nonzero reference line index is signaled. FIG.12 shows an example of four reference lines for a CB (1210). Referringto FIG. 12, a reference line can include up to six segments, e.g.,Segments A to F, and a top-left reference sample. For example, thereference line 0 includes the Segments B and E and a top-left referencesample. For example, the reference line 3 includes the Segments A to Fand a top-left reference sample. The Segment A and F can be padded withclosest samples from the Segment B and E, respectively. In someexamples, such as in the HEVC, only one reference line (e.g., thereference line 0 that is adjacent to the CB (1210)) is used for intraprediction. In some examples, such as in the VVC, multiple referencelines (e.g., the reference lines 0, 1, and 3) are used for intraprediction.

In general, a block can be predicted using one or a suitable combinationof various intra prediction modes such as described above withreferences to FIGS. 9-12.

Transform block partition (also referred to as transform partition,transform unit partition) can be implemented to partition a block intomultiple TUs or multiple TBs. FIGS. 13-14 show exemplary transform blockpartitions according to embodiments of the disclosure. In some examples,such as in AV1, both intra coded blocks and inter coded blocks can befurther partitioned into multiple transform units with a partitioningdepth up to multiple levels (e.g., 2 levels). The multiple transformunits resulting from the transform block partition can be referred to asTBs. A transform (e.g., a primary transform and/or a secondary transformsuch as described below) can be performed on each of the multiple TUs orthe multiple TBs. Accordingly, multiple transforms can be performed onthe block that is partitioned into the multiple transform units ormultiple TBs.

For an intra coded block, the transform partition can be performed suchthat transform blocks associated with the intra coded block have a samesize, and the transform blocks can be coded in a raster scan order.Referring to FIG. 13, transform block partition can be performed on ablock (e.g., an intra coded block) (1300). The block (1300) can bepartitioned into transform units, such as four transform units (e.g.,TBs) (1301)-(1304), and a partitioning depth is 1. The four transformunits (e.g., TBs) (1301)-(1304) can have a same size, and can be codedin a raster scan order (1310) from the transform unit (1301) to thetransform unit (1304). In an example, the four transform units (e.g.,TBs) (1301)-(1304) are transformed separately, for example, usingdifferent transform kernels. In some examples, each of the fourtransform units (e.g., TBs) (1301)-(1304) is further partitioned intofour transform unit. For example, the transform unit (1301) ispartitioned into transform units (1321), (1322), (1325), and (1326), thetransform unit (1302) is partitioned into transform units (1323),(1324), (1327), and (1328), the transform unit (1303) is partitionedinto transform units (1329), (1330), (1333), and (1334), and thetransform unit (1304) is partitioned into transform units (1331),(1332), (1335), and (1336). The partitioning depth is 2. The transformunits (e.g., TBs) (1321)-(1336) can have a same size, and can be codedin a raster scan order (1320) from the transform unit (1321) to thetransform unit (1336).

For inter coded blocks, the transform partition can be performed in arecursive manner with a partitioning depth up to multiple levels (e.g.,two levels). The transform partition can support any suitable transformunit sizes and shapes. The transform unit shapes can include a squareshape and a non-square shape (e.g., a non-square rectangular shape)having any suitable aspect ratio. The transform unit sizes can rangefrom 4×4 to 64×64. The aspect ratio of the transform unit (e.g., a ratioof a width of the transform unit over a height of the transform unit)can be 1:1 (square), 1:2, 2:1, 1:4, 4:1, or the like. The transformpartition can support 1:1 (square), 1:2, 2:1, 1:4, and/or 4:1 transformunit sizes ranging from 4×4 to 64×64. Referring to FIG. 14, transformblock partition can be performed on a block (e.g., an inter coded block)(1400) recursively. For example, the block (1400) is partitioned intotransform units (1401)-(1407). The transform units (e.g., TBs)(1401)-(1407) can have different sizes and can be coded in a raster scanorder (1410) from the transform unit (1401) to the transform unit(1407). In an example, partitioning depths of the transform units(1401), (1406), and (1407) are 1, and partitioning depths of thetransform units (1402)-(1405) are 2.

In an example, if a coding block is smaller than or equal to 64×64, thetransform partition can only be applied to a luma component. In anexample, the coding block refers to a CTB.

If a coding block width W or a coding block height H is greater than 64,the coding block can be implicitly split into multiple TBs where thecoding block is a luma coding block. A width of one of the multiple TBscan be a minimum of W and 64 and a height of the one of the multiple TBscan be a minimum of H and 64.

If the coding block width W or the coding block height H is greater than64, the coding block can be implicitly split into multiple TBs where thecoding block is a chroma coding block. A width of one of the multipleTBs can be a minimum of W and 32 and a height of the one of the multipleTBs can be a minimum of H and 32.

Embodiments of primary transforms, such as those used in AOMedia Video 1(AV1), are described below. A forward transform (e.g., in an encoder)can be performed on a transform block (TB) including residuals (e.g.,residuals in a spatial domain) to obtain a TB including transformcoefficients in a frequency domain (or a spatial frequency domain). TheTB including the residuals in the spatial domain can be referred to as aresidual TB and the TB including the transform coefficients in thefrequency domain can be referred to as a coefficient TB. In an example,the forward transform includes a forward primary transform that cantransform the residual TB into the coefficient TB. In an example, theforward transform includes a forward primary transform and a forwardsecondary transform where the forward primary transform can transformthe residual TB into an intermediate coefficient TB, and the forwardsecondary transform can transform the intermediate coefficient TB intothe coefficient TB.

An inverse transform (e.g., in an encoder or in a decoder) can beperformed on the coefficient TB in the frequency domain to obtain theresidual TB in the spatial domain. In an example, the inverse transformincludes an inverse primary transform that can transform the coefficientTB into the residual TB. In an example, the inverse transform includesan inverse primary transform and an inverse secondary transform wherethe inverse secondary transform can transform the coefficient TB intothe intermediate coefficient TB and the inverse primary transform cantransform the intermediate coefficient TB into the residual TB.

In general, a primary transform can refer to the forward primarytransform or the inverse primary transform where the primary transformis performed between the residual TB and the coefficient TB. In someembodiments, the primary transform can be a separable transform wherethe 2D primary transform can include a horizontal primary transform(also referred to as a horizontal transform) and a vertical primarytransform (also referred to as a vertical transform). A secondarytransform can refer to the forward secondary transform or the inversesecondary transform where the secondary transform is performed betweenthe intermediate coefficient TB and the coefficient TB.

In order to support extended coding block partitions, such as describedin the disclosure, multiple transform sizes (e.g., ranging from 4-pointto 64-point for each dimension) and transform shapes (e.g., square, arectangular shape with a width over a height ratio of 2:1, 1:2, 4:1, or1:4) can be used, such as in AV1.

A 2D transform process can use hybrid transform kernels that can includea different 1D transform for each dimension of a coded residual block.Primary 1D transforms can include (a) a 4-point, an 8-point, a 16-point,a 32-point, a 64-point DCT-2; (b) a 4-point, an 8-point, a 16-pointasymmetric DST (ADST) (e.g., a DST-4, a DST-7) and corresponding flippedversions (e.g., a flipped version or a FlipADST of an ADST can apply theADST in a reverse order); and/or (c) a 4-point, an 8-point, a 16-point,a 32-point identity transform (IDTX). FIG. 15 shows examples of primarytransform basis functions according to embodiments of the disclosure.The primary transform basis functions in the FIG. 15 example includebasis functions for the DCT-2 and the asymmetric DSTs (DST-4 and DST-7)having an N-point input. The primary transform basis functions shown inFIG. 15 can be used in AV1.

The availability of hybrid transform kernels can be dependent on atransform block size and a prediction mode. FIG. 16A shows exemplarydependencies of the availability of various transform kernels (e.g.,transform types shown in the first column and described in the secondcolumn) based on the transform block size (e.g., sizes shown in thethird column) and the prediction mode (e.g., the intra prediction andthe inter prediction shown in the third column). The exemplary hybridtransform kernels and the availability based on the prediction modes andtransform block sizes can be used in AV1. Referring to FIG. 16A, symbols“→” and “↓” denote a horizontal dimension (also referred to as ahorizontal direction) and a vertical dimension (also referred to as avertical direction), respectively. Symbols “✓” and “x” denote theavailability of a transform kernel for the corresponding block size andthe prediction mode. For example, the symbol “✓” denotes that thetransform kernel is available, and the symbol “x” denotes that thetransform kernel is unavailable.

In an example, a transform type (1610) is denoted by ADST_DCT as shownin the first column of FIG. 16A. The transform type (1610) includes anADST in the vertical direction and a DCT in the horizontal direction asshown in the second column of FIG. 16A. According to the third column ofFIG. 16A, the transform type (1610) is available for the intraprediction and the inter prediction when the block size is less than orequal to 16×16 (e.g., 16×16 samples, 16×16 luma samples).

In an example, a transform type (1620) is denoted by V_ADST as shown inthe first column of FIG. 16A. The transform type (1620) includes an ADSTin the vertical direction and an IDTX (i.e., an identity matrix) in thehorizontal direction as shown in the second column of FIG. 16A. Thus,the transform type (1620) (e.g., V_ADST) is performed in the verticaldirection and is not performed in the horizontal direction. According tothe third column of FIG. 16A, the transform type (1620) is not availablefor the intra prediction regardless of the block size. The transformtype (1620) is available for the inter prediction when the block size isless than 16×16 (e.g., 16×16 samples, 16×16 luma samples).

In an example, FIG. 16A is applicable for a luma component. For a chromacomponent, a transform type (or a transform kernel) selection can beperformed implicitly. In an example, for intra prediction residuals, thetransform type can be selected according to an intra prediction mode, asshown in FIG. 16B. In an example, transform type selections shown inFIG. 16 B are applicable to a chroma component. For inter predictionresiduals, the transform type can be selected according to the transformtype selection of a co-located luma block. Therefore, in an example, atransform type for the chroma component is not signaled in a bitstream.

Line graph transforms (LGT) can be used in transforms such as a primarytransform, for example, in AOMedia Video 2 (AV2). 8-bit/10-bit transformcores can be used in AV2. In an example, LGTs include various DCTs,discrete sine transforms (DSTs), as described below. LGTs can include32-point and 64-point 1-dimensional (1D) DSTs.

Graphs are generic mathematical structures including sets of verticesand edges that can be used for modelling affinity relations betweenobjects of interest. Weighted graphs where a set of weights are assignedto edges and optionally to vertices can provide sparse representationsfor robust modeling of signals/data. LGTs can improve coding efficiencyby providing a better adaptation for diverse block statistics. SeparableLGTs can be designed and optimized by learning line graphs from data tomodel underlying row and column-wise statistics of residual signals of ablock, and associated generalized graph Laplacian (GGL) matrices can beused to derive the LGTs.

FIG. 16C shows an example of a generic LGT characterized by self-loopweights (e.g., v_(c1), v_(c2)) and edge weights w_(c) according to anembodiment of the disclosure. Given a weighted graph G (W, V), the GGLmatrix can be defined as below.

L _(c) =D−W+V  (Eq. 3)

where W can be an adjacency matrix including the non-negative edgeweights w_(c), D can be a diagonal degree matrix, and V can be adiagonal matrix denoting the self-loop weights v_(c1) and v_(c2). FIG.16D shows an example of the matrix L_(c).

The LGT can be derived by an Eigen-decomposition of the GGL matrix L_(c)as below.

L _(c) =UΦU ^(T)  (Eq. 4)

where columns of an orthogonal matrix U can be the basis vectors of theLGT, and Φ can be a diagonal eigenvalue matrix.

In various examples, certain DCTs and DSTs (e.g., DCT-2, DCT-8, andDST-7), are subsets of a set of LGTs derived from certain forms of theGGLs. The DCT-2 can be derived by setting v_(c1) to 0 (e.g., v_(c1)=0).The DST-7 can be derived by setting v_(c1) to w_(c) (e.g.,v_(c1)=w_(e)). The DCT-8 can be derived by setting v_(c2) to w_(c)(e.g., v_(c2)=w_(c)). The DST-4 can be derived by setting v_(c1) to2w_(c) (e.g., v_(c1)=2w_(c)). The DCT-4 can be derived by setting v_(c2)to 2w_(c) (e.g., v_(c2)=2w_(c)).

In some examples, such as in AV2, the LGTs can be implemented as matrixmultiplications. A 4-point (4p) LGT core can be derived by settingv_(c1) to 2w_(c) in Lc, and thus the 4p LGT core is the DST-4. An8-point (8p) LGT core can be derived by setting v_(c1) to 1.5w_(c) inLc. In an example, an LGT core, such as a 16-point (16p) LGT core, a32-point (32p) LGT core, or a 64-point (64p) LGT core, can be derived bysetting v_(c1) to be w_(c) and v_(c2) to be 0 and the LGT core canbecome DST-7.

A transform, such as a primary transform, a secondary transform, can beapplied to a block such as a CB. In an example, a transform includes acombination of a primary transform, a secondary transform. A transformcan be a non-separable transform, a separable transform, or acombination of a non-separable transform and a separable transform.

A secondary transform can be performed such as in VVC. In some examples,such as in VVC, a low-frequency non-separable transform (LFNST), whichis also known as a reduced secondary transform (RST), can be appliedbetween a forward primary transform and quantization at an encoder sideand between de-quantization and an inverse primary transform at adecoder side as shown in FIGS. 17-18 to further de-correlate primarytransform coefficients.

Application of a non-separable transform, which can be used in an LFNST,can be described as follows using a 4×4 input block (or an input matrix)X as an example (shown in Eq. 5). To apply the 4×4 non-separabletransform (e.g., the LFNST), the 4×4 input block X can be represented bya vector

, as shown in Eqs. 5-6.

$\begin{matrix}{X = \begin{bmatrix}X_{00} & X_{01} & X_{02} & X_{03} \\X_{10} & X_{11} & X_{12} & X_{13} \\X_{20} & X_{21} & X_{22} & X_{23} \\X_{30} & X_{31} & X_{32} & X_{33}\end{bmatrix}} & ( {{Eq}.\mspace{14mu} 5} )\end{matrix}$

=[X ₀₀ X ₀₁ X ₀₂ X ₀₃ X ₁₀ X ₁₁ X ₁₂ X ₁₃ X ₂₀ X ₂₁ X ₂₂ X ₂₃ X ₃₀ X ₃₁X ₃₂ X ₃₃]^(T)  (Eq. 6)

The non-separable transform can be calculated as

=T·

, where

indicates a transform coefficient vector, and T is a 16×16 transformmatrix. The 16×1 coefficient vector

can be subsequently reorganized into a 4×4 output block (or an outputmatrix, a coefficient block) using a scanning order (e.g., a horizontalscanning order, a vertical scanning order, a zigzag scanning order, or adiagonal scanning order) for the 4×4 input block. The transformcoefficients with smaller indices can be placed with smaller scanningindices in the 4×4 coefficient block.

A non-separable secondary transform can be applied to a block (e.g., aCB). In some examples, such as in the VVC, the LFNST is applied betweena forward primary transform and quantization (e.g., at an encoder side)and between de-quantization and an inverse primary transform (e.g., at adecoder side) as shown in FIGS. 17-18.

FIGS. 17-18 show examples of two transform coding processes (1700) and(1800) using a 16×64 transform (or a 64×16 transform depending onwhether the transform is a forward or inverse secondary transform) and a16×48 transform (or a 48×16 transform depending on whether the transformis a forward or inverse secondary transform), respectively. Referring toFIG. 17, in the process (1700), at an encoder side, a forward primarytransform (1710) can first be performed over a block (e.g., a residualblock) to obtain a coefficient block (1713). Subsequently, a forwardsecondary transform (or a forward LFNST) (1712) can be applied to thecoefficient block (1713). In the forward secondary transform (1712), 64coefficients of 4×4 sub-blocks A-D at a top-left corner of thecoefficient block (1713) can be represented by a 64-length vector, andthe 64-length vector can be multiplied with a transform matrix of 64×16(i.e., a width of 64 and a height of 16), resulting in a 16-lengthvector. Elements in the 16-length vector are filled back into thetop-left 4×4 sub-block A of the coefficient block (1713). Thecoefficients in the sub-blocks B-D can be zero. The resultingcoefficients after the forward secondary transform (1712) are thenquantized at a quantization step (1714), and entropy-coded to generatecoded bits in a bitstream (1716).

The coded bits can be received at a decoder side, and entropy-decodedfollowed by a de-quantization step (1724) to generate a coefficientblock (1723). An inverse secondary transform (or an inverse LFNST)(1722), such as an inverse RST8×8, can be performed to obtain 64coefficients, for example, from the 16 coefficients at a top-left 4×4sub-block E. The 64 coefficients can be filled back to the 4×4sub-blocks E-H. Further, the coefficients in the coefficient block(1723) after the inverse secondary transform (1722) can be processedwith an inverse primary transform (1720) to obtain a recovered residualblock.

The process (1800) of the FIG. 18 example is similar to the process(1700) except that fewer (i.e., 48) coefficients are processed duringthe forward secondary transform (1712). Specifically, the 48coefficients in the sub-blocks A-C are processed with a smallertransform matrix of a size of 48×16. Using the smaller transform matrixof 48×16 can reduce a memory size for storing the transform matrix and anumber of calculations (e.g., multiplications, additions, subtractions,and/or the like), and thus can reduce computation complexity.

In an example, a 4×4 non-separable transform (e.g., a 4×4 LFNST) or an8×8 non-separable transform (e.g., an 8×8 LFNST) is applied according toa block size of the block (e.g., the CB). The block size of the blockcan include a width, a height, or the like. For example, the 4×4 LFNSTis applied for the block where a minimum of the width and the height isless than a threshold, such as 8 (e.g., min (the width, the height)<8).For example, the 8×8 LFNST is applied for the block where the minimum ofthe width and the height is larger than a threshold, such as 4 (e.g.,min (width, height)>4).

A non-separable transform (e.g., the LFNST) can be based on a directmatrix multiplication approach, and thus can be implemented in a singlepass without iteration. To reduce a non-separable transform matrixdimension and to minimize computational complexity and memory space tostore transform coefficients, a reduced non-separable transform method(or RST) can be used in the LFNST. Accordingly, in the reducednon-separable transform, an N (e.g., N is 64 for an 8×8 non-separablesecondary transform (NSST)) dimensional vector can be mapped to an Rdimensional vector in a different space, where N/R (R<N) is a reductionfactor. Hence, instead of an N×N matrix, an RST matrix is an R×N matrixas described in Eq. 7.

$\begin{matrix}{T_{R \times N} = \begin{bmatrix}t_{11} & t_{12} & t_{13} & \ldots & t_{1N} \\t_{21} & t_{22} & t_{23} & \; & t_{2N} \\\; & \vdots & \; & \ddots & \vdots \\t_{R\; 1} & t_{R\; 2} & t_{R\; 3} & \ldots & t_{RN}\end{bmatrix}} & ( {{Eq}.\mspace{14mu} 7} )\end{matrix}$

In Eq. 7, R rows of the R×N transform matrix are R bases of the Ndimensional space. The inverse transform matrix can be a transpose ofthe transform matrix (e.g., T_(R×N)) used in the forward transform. Foran 8×8 LFNST, a reduction factor of 4 can be applied, and a 64×64 directmatrix used in an 8×8 non-separable transform can be reduced to a 16×64direct matrix, as shown in FIG. 17. Alternatively, a reduction factorlarger than 4 can be applied, and the 64×64 direct matrix used in the8×8 non-separable transform can be reduced to a 16×48 direct matrix, asshown in FIG. 18. Hence, a 48×16 inverse RST matrix can be used at adecoder side to generate core (primary) transform coefficients in an 8×8top-left region.

Referring to FIG. 18, when the 16×48 matrix is applied instead of the16×64 matrix with a same transform set configuration, an input to the16×48 matrix includes 48 input data from three 4×4 blocks A, B, and C ina top-left 8×8 block excluding a right-bottom 4×4 block D. With areduction in the dimension, a memory usage for storing LFNST matricescan be reduced, for example, from 10 KB to 8 KB with a minimalperformance drop.

In order to reduce complexity, the LFNST can be restricted to beapplicable if coefficients outside a first coefficient subgroup arenon-significant. In an example, the LFNST can be restricted to beapplicable only if all coefficients outside the first coefficientsubgroup are non-significant. Referring to FIGS. 17-18, the firstcoefficient subgroup corresponds to the top-left block E, and thus thecoefficients that are outside the block E are non-significant.

In an example, primary-only transform coefficients are non-significant(e.g., zero) when the LFNST is applied. In an example, all primary-onlytransform coefficients are zero when the LFNST is applied. Theprimary-only transform coefficients can refer to transform coefficientsthat are obtained from a primary transform without a secondarytransform. Accordingly, an LFNST index signaling can be conditioned on alast-significant position, and thus avoiding an extra coefficientscanning in the LFNST. In some examples, the extra coefficient scanningis used to check significant transform coefficients at specificpositions. In an example, the worst-case handling of the LFNST, forexample, in terms of multiplications per pixel restricts thenon-separable transform for a 4×4 block and an 8×8 block to an 8×16transform and an 8×48 transform, respectively. In the above cases, thelast-significant scan position can be less than 8 when the LFNST isapplied. For other sizes, the last-significant scan position can be lessthan 16 when the LFNST is applied. For a CB of 4×N and N×4 and N islarger than 8, the restriction can imply that the LFNST is applied to atop-left 4×4 region in the CB. In an example, the restriction impliesthat the LFNST is applied only once to the top-left 4×4 region only inthe CB. In an example, all the primary-only coefficients arenon-significant (e.g., zero) when the LFNST is applied, a number ofoperations for the primary transform is reduced. From an encoderperspective, quantization of transform coefficients can be significantlysimplified when the LFNST transform is tested. A rate-distortionoptimized quantization can be done at maximum for the first 16coefficients, for example, in a scanning order, remaining coefficientscan be set to zero.

An LFNST transform (e.g., a transform kernel, a transform core, or atransform matrix) can be selected as described below. In an embodiment,multiple transform sets can be used, and one or more non-separabletransform matrices (or kernels) can be included in each of the multipletransform sets in the LFNST. According to aspects of the disclosure, atransform set can be selected from the multiple transform sets, and anon-separable transform matrix can be selected from the one or morenon-separable transform matrices in the transform set.

Table 1 shows an exemplary mapping from intra prediction modes to themultiple transform sets according to an embodiment of the disclosure.The mapping indicates a relationship between the intra prediction modesand the multiple transform sets. The relationship, such as indicated inTable 1, can be pre-defined and can be stored in an encoder and adecoder.

TABLE 1 Transform set selection table IntraPredMode Tr. set indexIntraPredMode < 0 1  0 <= IntraPredMode <= 1 0  2 <= IntraPredMode <= 121 13 <= IntraPredMode <= 23 2 24 <= IntraPredMode <= 44 3 45 <=IntraPredMode <= 55 2 56 <= IntraPredMode <= 80 1 81 <= IntraPredMode <=83 0

Referring to Table 1, the multiple transform sets include four transformsets, e.g., transform sets 0 to 3 represented by a transform set index(e.g., Tr. set index) from 0 to 3, respectively. An index (e.g., anIntraPredMode) can indicate the intra prediction mode, and the transformset index can be obtained based on the index and Table 1. Accordingly,the transform set can be determined based on the intra prediction mode.In an example, if one of three cross component linear model (CCLM) modes(e.g., INTRA_LT_CCLM, INTRA_T_CCLM or INTRA_L_CCLM) is used for a CB(e.g., 81<=IntraPredMode<=83), the transform set 0 is selected for theCB.

As described above, each transform set can include the one or morenon-separable transform matrices. One of the one or more non-separabletransform matrices can be selected by an LFNST index that is, forexample, explicitly signaled. The LFNST index can be signaled in abitstream once per intra-coded CU (e.g., the CB), for example, aftersignaling transform coefficients. In an embodiment, each transform setincludes two non-separable transform matrices (kernels), and theselected non-separable secondary transform candidate can be one of thetwo non-separable transform matrices. In some examples, the LFNST is notapplied to a CB (e.g., the CB coded with a transform skip mode or anumber of non-zero coefficients of the CB is less than a threshold). Inan example, the LFNST index is not signaled for the CB when the LFNST isnot to be applied to the CB. A default value for the LFNST index can bezero and not signaled, indicating that the LFNST is not applied to theCB.

In an embodiment, the LFNST is restricted to be applicable only if allcoefficients outside the first coefficient subgroup are non-significant,coding of the LFNST index can depend on a position of the lastsignificant coefficient. The LFNST index can be context coded. In anexample, the context coding of the LFNST index does not depend on anintra prediction mode, and only a first bin is context coded. The LFNSTcan be applied to an intra-coded CU in an intra slice or in an interslice, and for both Luma and Chroma components. If a dual tree isenabled, LFNST indices for Luma and Chroma components can be signaledseparately. For an inter slice (e.g., the dual tree is disabled), asingle LFNST index can be signaled and used for both the Luma and Chromacomponents.

Intra sub-partition (ISP) coding mode can be used. In the ISP codingmode, a luma intra-predicted block can be divided vertically orhorizontally into 2 or 4 sub-partitions depending on a block size. Insome examples, performance improvement is marginal when the RST isapplied to every feasible sub-partition. Thus, in some examples, when anISP mode is selected, the LFNST is disabled and the LFNST index (or anRST index) is not signaled. Disabling the RST or the LFNST forISP-predicted residues can reduce coding complexity. In some examples,the LFNST is disabled and the LFNST index is not signaled when amatrix-based intra predication mode (MIP) is selected.

In some example, a CU larger than 64×64 is implicitly split (TU tiling)due to a maximum transform size restriction (e.g., 64×64), an LFNSTindex search can increase data buffering by four times for a certainnumber of decode pipeline stages. Therefore, the maximum size that theLFNST is allowed can be restricted to 64×64. In an example, the LFNST isenabled with a discrete cosine transform (DCT) type 2 (DCT-2) transformonly.

In some examples, separable transform schemes may not be efficient forcapturing directional texture patterns (e.g., edges which are along a45° or a 135° direction). A non-separable transform scheme may improvecoding efficiency, for example, in the above scenarios. To reducecomputational complexity and memory usage, the non-separable transformscheme can be used as a secondary transform that is applied to lowfrequency transform coefficients that are obtained from a primarytransform. The secondary transform can be applied to a block andinformation, for example, an index (e.g., a secondary transform index)indicating the secondary transform can be signaled for the block basedon prediction mode information, a primary transform type, neighboringreconstructed samples, transform block partitioning information, a sizeand a shape of the block, and/or the like. One or a combination of theprediction mode information, the primary transform type, and the size ofthe block (or the block size) can be utilized to derive contextinformation. The context information can be used to determine context(s)to be used for entropy coding a secondary transform index used toidentify a secondary transform among a set of secondary transforms(e.g., a set of non-separable secondary transforms). The secondarytransform index can be used in decoding the block.

In the disclosure, the term block may refer to a PB, a CB, a codedblock, a coding unit (CU), a transform block (TB), a transform unit(TU), a luma block (e.g., a luma CB), a chroma block (e.g., a chromaCB), or the like.

The size of a block can refer to a block width, a block height, a blockaspect ratio (e.g., a ratio of a block width over a block height, aratio of a block height over a block width), a block area size or ablock area (e.g., a block width×a block height), a minimum of a blockwidth and a block height, a maximum of a block width and a block height,and/or the like.

Information indicating a secondary transform (e.g., a secondarytransform kernel, a secondary transform core, or a secondary transformmatrix) used for coding (e.g., encoding and/or decoding) the block caninclude an index (e.g., a secondary transform index). As discussedabove, in an embodiment, multiple transform sets can be used, and one ormore secondary transform matrices (or kernels) can be included in eachof the multiple transform sets. According to aspects of the disclosure,a transform set can be selected from the multiple transform sets usingany suitable method including but not limited to that described withreference to Table 1, and the secondary transform (e.g., the secondarytransform matrix) used to code (e.g., encode and/or decode) the blockcan be determined (e.g., selected) from the one or more secondarytransform matrices in the transform set by the index (e.g., thesecondary transform index). The index (e.g., the secondary transformmatrix) can be used to identify one secondary transform among atransform set of secondary transforms used for decoding the block. In anexample, the transform set of secondary transforms includes a set ofnon-separable secondary transforms used for decoding the block. In anexample, the index (e.g., the secondary transform matrix) is denoted asstIdx. The index (e.g., the secondary transform index) can be explicitlysignaled, for example, in the coded video bitstream.

In an example, the secondary transform is an LFNST, and the secondarytransform index refers to an LFNST index. In some examples, thesecondary transform is not applied to the block (e.g., a CB coded with atransform skip mode or a number of non-zero coefficients of the CB isless than a threshold). In an example, the secondary transform index(e.g., the LFNST index) is not signaled for the block when the secondarytransform is not to be applied to the block. A default value for thesecondary transform index can be zero and not signaled, indicating thatthe secondary transform is not applied to the block.

According to aspects of the disclosure, coded information for a block(e.g., a TB) can be decoded from a coded video bitstream. The codedinformation can indicate one or more of prediction mode information forthe block, a size of the block, and a primary transform type used forthe block. The primary transform type can refer to any suitable primarytransform, such as one or a combination of those described withreferences to FIGS. 15 and 16A-16D.

In an example, the block is intra coded or intra predicted, and theprediction mode information is referred to as intra prediction modeinformation. The prediction mode information (e.g., the intra predictionmode information) for the block can indicate an intra prediction modeused for the block. The intra prediction mode can refer to a predictionmode used for intra prediction of the block, such as a directional mode(or a directional prediction mode) described in FIG. 9, anon-directional prediction mode (e.g., the DC mode, the PAETH mode, theSMOOTH mode, the SMOOTH_V mode, or the SMOOTH_H mode) described in FIG.10, or a recursive filtering mode described in FIG. 11. The intraprediction mode can also refer to a prediction mode described in thedisclosure, a suitable variation of a prediction mode that is describedin the disclosure, or a suitable combination of prediction modesdescribed in the disclosure. For example, the intra prediction mode canbe combined with multi-line intra prediction described in FIG. 12.

The coded information, such as the one or more of the prediction modeinformation for the block, the size of the block, and the primarytransform type used for the block, can be used as a context for entropycoding (e.g., entropy encoding and/or entropy decoding) a secondarytransform index (e.g., stIdx). The context for entropy coding (e.g.,entropy encoding and/or entropy decoding) the secondary transform indexcan be determined based on the coded information, such as the one ormore of the prediction mode information for the block, the size of theblock, and the primary transform type used for the block. The secondarytransform index (e.g., stIdx) can indicate a secondary transform in aset of secondary transforms that is to be performed on the block.

A context derivation process can be used to determine the context. Thecontext derivation process for entropy coding (e.g., encoding and/ordecoding) the secondary transform index can depend on the codedinformation.

The context for entropy coding (e.g., encoding and/or decoding) thesecondary transform index can be determined based on the one or more ofthe prediction mode information (e.g., the intra prediction modeinformation) for the block, the size of the block, and the primarytransform type used for the block. In an example, the context forentropy coding (e.g., encoding and/or decoding) the secondary transformindex is determined based on one of the prediction mode information(e.g., the intra prediction mode information) for the block, the size ofthe block, and the primary transform type used for the block. Thesecondary transform index can be entropy coded (e.g., encoded and/ordecoded) based on the context. The secondary transform (e.g., an inversesecondary transform) indicated by the secondary transform index can beperformed on the block (e.g., the TB).

In an embodiment, the context derivation process for entropy coding(e.g., encoding and/or decoding) the secondary transform index (e.g.,the stIdx) can depend on the size of the block. In an example, a largestsquare block size associated with the block refers to a size of alargest square block in the block. The largest square block size is lessthan or equal to the size of the block. In an example, the size of theblock is a TB size when the block refers to a TB. The largest squareblock size can be used in the context derivation process. In an example,the largest square block size is used as the context. For example, thesize of the block can indicate a block width W and a block height H. Thelargest square block size is L×L where L is a minimum of W and H. Thelargest square block size can also be indicated by L. If W is 32, H is8, L is 8. The largest square block size can be indicated by 8 or 8×8.

In an embodiment, the one of the intra prediction mode information forthe block, the size of the block, and the primary transform type usedfor the block can indicate the size of the block. The context forentropy coding (e.g., encoding and/or decoding) the secondary transformindex can be determined based on the size of the block. In an example,the size of the block indicates the width W of the block and the heightH of the block. A minimum of the width W of the block and the height Hof the block is denoted as L. The context can be determined based on thelargest square block size L or L×L. In an example, the largest squareblock size L or L×L is used as the context.

In an embodiment, the context derivation process for entropy coding(e.g., encoding and/or decoding) the secondary transform index (e.g.,the stIdx) can depend on the prediction mode information (e.g., theintra prediction mode information) for the block. The context forentropy coding (e.g., encoding and/or decoding) the secondary transformindex can be derived based on the prediction mode information (e.g., theintra prediction mode information) for the block.

In an example, the block is intra predicted using one of the directionalmodes (also referred to as the directional prediction modes), such asdescribed with reference to FIG. 9. Referring to FIG. 9, a nominal modeindex can indicate a nominal mode (e.g., one of the eight nominalmodes). In an example, a directional mode (e.g., one of the 56directional modes) can be determined based on the nominal mode index andan index indicating an angular offset from the nominal mode. Theprediction mode information (e.g., the intra prediction modeinformation) for the block can indicate the nominal mode index. Thenominal mode index can be used for the context derivation process. Thecontext for entropy coding (e.g., encoding and/or decoding) thesecondary transform index can be derived based on the nominal modeindex.

In an embodiment, the one of the intra prediction mode information forthe block, the size of the block, and the primary transform type usedfor the block can indicate the intra prediction mode information for theblock. The context for entropy coding (e.g., encoding and/or decoding)the secondary transform index can be determined based on the intraprediction mode information for the block. In an example, the intraprediction mode information for the block indicates the nominal modeindex. The block can be predicted using the directional prediction modethat is determined based on the nominal mode index and the angularoffset, as described above. The context for entropy coding (e.g.,encoding and/or decoding) the secondary transform index can bedetermined based on the nominal mode index.

In an embodiment, the block is intra predicted using the directionalmode as described above. The nominal mode index can be mapped to anindex value that is different from the nominal mode index, and the indexvalue can be used in the context derivation process. In an example,multiple intra prediction modes (e.g., multiple nominal modes shown inFIG. 9) can be mapped to the same index value. The multiple nominalmodes (or multiple nominal mode indices corresponding to the multiplenominal modes) can be mapped to the same index value. The multiplenominal modes can be adjacent to each other. Referring to FIG. 9,D67_PRED and D45_PRED can be mapped to a same index value.

In an embodiment, the intra prediction mode information for the blockindicates the nominal mode index, the block can be predicted using thedirectional mode (or the directional prediction mode) that is determinedbased on the nominal mode index and the angular offset. The context forentropy coding (e.g., encoding and/or decoding) the secondary transformindex can be determined based on the index value associated with thenominal mode index (e.g., the nominal mode index is mapped to the indexvalue).

In an embodiment, the block is intra predicted using one of thenon-directional prediction modes (also referred to as thenon-directional smooth intra prediction modes) including, for example,the DC mode, the PAETH mode, the SMOOTH mode, the SMOOTH_V mode, and theSMOOTH_H mode, as described with reference to FIG. 10. A correspondingmode index (also referred to as a non-directional prediction mode index)indicating the one of the non-directional prediction modes can be usedfor the context derivation process. In an example, the same context canbe applied to entropy code the secondary transform index (e.g., thestIdx) for one or more of the non-directional prediction modes. The samecontext can correspond to a plurality of the non-directional predictionmodes.

In an embodiment, the intra prediction mode information for the blockcan indicate the non-directional prediction mode index. The block can bepredicted using the one of the non-directional prediction modes (e.g., anon-directional prediction mode) indicated by the non-directionalprediction mode index. The context for entropy coding (e.g., encodingand/or decoding) the secondary transform index can be determined basedon the non-directional prediction mode index.

In an example, the block is intra predicted using one of the recursivefiltering modes, such as described with reference to FIG. 11. A mappingcan be first performed from the one of the recursive filtering mode to anominal mode index where the nominal mode index can indicate a nominalmode (e.g., one of the eight nominal modes in FIG. 9). The nominal modeindex can be subsequently used for the context derivation process. In anexample, the same context can be applied to entropy code (e.g., encodeand/or decode) the secondary transform index (e.g., the stIdx) for oneor more of the recursive filtering modes. The same context cancorrespond to a plurality of the recursive filtering modes.

In an embodiment, the intra prediction mode information for the blockcan indicate a recursive filtering mode (one of the recursive filteringmodes) used to predict the block. A nominal mode index indicating anominal mode can be determined based on the recursive filtering mode.The context for entropy coding (e.g., encoding and/or decoding) thesecondary transform index can be determined based on the nominal modeindex.

In an embodiment, the context derivation process for entropy coding thesecondary transform index (e.g., the stIdx) can depend on primarytransform type information. The primary transform type information canindicate the primary transform type or a type of a primary transformused for the block. In an example, the context is determined based onthe primary transform type. In an example, the context is determinedbased on the primary transform.

In an embodiment, the one of the intra prediction mode information forthe block, the size of the block, and the primary transform type usedfor the block indicates the primary transform type used for the block.The context for entropy coding (e.g., encoding and/or decoding) thesecondary transform index can be determined based on the primarytransform type used for the block. The context for entropy coding thesecondary transform index can be determined based on the primarytransform used for the block.

In an embodiment, a primary transform for the block can include ahorizontal primary transform (referred to as a horizontal transform) anda vertical primary transform (referred to as a vertical transform). Thecontext for entropy coding (e.g., encoding and/or decoding) thesecondary transform index can be determined based on the horizontalprimary transform type and the vertical primary transform type. Thehorizontal primary transform type can indicate the horizontal transformand the vertical primary transform type can indicate the verticaltransform.

The context (also referred to as a context value) can depend on whetherboth the horizontal primary transform type and the vertical primarytransform type are DCTs or both the horizontal primary transform typeand the vertical primary transform type are ADSTs.

In the disclosure, a combination of the horizontal primary transformtype and the vertical primary transform type can be represented as {thehorizontal primary transform type, the vertical primary transform type}.Thus, {DCT, DCT} represents both the horizontal primary transform typeand the vertical primary transform type being DCTs. {ADST, ADST}represents both the horizontal primary transform type and the verticalprimary transform type being ADSTs. {LGT, LGT} represents both thehorizontal primary transform type and the vertical primary transformtype being LGTs. {DCT, LGT} represents the horizontal primary transformtype being DCT and the vertical primary transform type being LGT. {LGT,DCT} represents the horizontal primary transform type being LGT and thevertical primary transform type being DCT.

In an embodiment, the primary transform indicated by the primarytransform type includes the horizontal transform indicated by thehorizontal primary transform type and the vertical transform indicatedby the vertical primary transform type. The context for entropy coding(e.g., encoding and/or decoding) the secondary transform index can bedetermined based on whether the horizontal primary transform type andthe vertical primary transform type are both DCTs or both ADSTs.

In an embodiment, the context can depend on whether the combination ofthe horizontal and vertical primary transform types is {DCT, DCT} or{LGT, LGT}.

In an embodiment, the primary transform indicated by the primarytransform type includes the horizontal transform indicated by thehorizontal primary transform type and the vertical transform indicatedby the vertical primary transform type. The context for entropy coding(e.g., encoding and/or decoding) the secondary transform index can bedetermined based on whether the horizontal primary transform type andthe vertical primary transform type are both DCTs or are both LGTs.

In an embodiment, the context can depend on whether the combination ofthe horizontal and vertical primary transform type is {DCT, DCT}, {LGT,LGT}, {DCT, LGT}, or {LGT, DCT}.

In an embodiment, the primary transform indicated by the primarytransform type includes the horizontal transform indicated by thehorizontal primary transform type and the vertical transform indicatedby the vertical primary transform type. The context for entropy coding(e.g., encoding and/or decoding) the secondary transform index can bedetermined based on whether the horizontal primary transform type andthe vertical primary transform type are (i) both DCTs, (ii) both LGTs,(iii) a DCT and an LGT, respectively, or (iv) an LGT and a DCT,respectively.

In an embodiment, the context can depend on whether a combination of thehorizontal and vertical primary transform type is {DCT, DCT}, {LGT,LGT}, {DCT, IDTX} or {IDTX, DCT}, wherein IDTX represents an identitytransform. {DCT, IDTX} represents the horizontal primary transform typebeing DCT and the vertical primary transform type being IDTX. {IDTX,DCT} represents the horizontal primary transform type being IDTX and thevertical primary transform type being DCT.

In an embodiment, the primary transform indicated by the primarytransform type includes the horizontal transform indicated by thehorizontal primary transform type and the vertical transform indicatedby the vertical primary transform type. The context for entropy coding(e.g., encoding and/or decoding) the secondary transform index can bedetermined based on whether the horizontal primary transform type andthe vertical primary transform type are (i) both DCTs, (ii) both LGTs,(iii) a DCT and an identity transform (IDTX), respectively, or (iv) anIDTX and a DCT, respectively.

FIG. 19 shows a flow chart outlining a process (1900) according to anembodiment of the disclosure. The process (1900) can be used in thereconstruction of a block, such as a CB, a TB, a luma CB, a luma TB, achroma CB, a chroma TB, or the like. In various embodiments, the process(1900) are executed by processing circuitry, such as the processingcircuitry in the terminal devices (310), (320), (330) and (340), theprocessing circuitry that performs functions of the video encoder (403),the processing circuitry that performs functions of the video decoder(410), the processing circuitry that performs functions of the videodecoder (510), the processing circuitry that performs functions of thevideo encoder (603), and the like. In some embodiments, the process(1900) is implemented in software instructions, thus when the processingcircuitry executes the software instructions, the processing circuitryperforms the process (1900). The process starts at (S1901) and proceedsto (S1910).

At (S1910), coded information for a block (e.g., a TB, a luma TB, anintra coded TB, a CB) can be decoded from a coded video bitstream. Thecoded information can indicate one of intra prediction mode informationfor the block, a size of the block, and a primary transform type usedfor the block. The coded information can indicate one or more of theintra prediction mode information for the block, the size of the block,and the primary transform type used for the block.

The intra prediction mode information for the block can indicate anintra prediction mode used for intra prediction of the block, such as adirectional mode, a non-directional prediction mode, or a recursivefiltering mode described with references to FIGS. 9-11. The primarytransform type indicates a primary transformed used for the block.Examples of the primary transform type used for the block are describedin FIGS. 15 and 16A-16D.

At (S1920), a context for entropy decoding a secondary transform indexcan be determined based on the one of the intra prediction modeinformation for the block, the size of the block, and the primarytransform type used for the block. The secondary transform index canindicate a secondary transform in a set of secondary transforms wherethe secondary transform is to be performed on the block.

In an example, the context for entropy decoding the secondary transformindex can be determined based on the one or more of the intra predictionmode information for the block, the size of the block, and the primarytransform type used for the block.

In an example, the one of the intra prediction mode information for theblock, the size of the block, and the primary transform type used forthe block indicates the size of the block, and the context for entropydecoding the secondary transform index can be determined based on thesize of the block.

In an example, the one of the intra prediction mode information for theblock, the size of the block, and the primary transform type used forthe block indicates the intra prediction mode information for the blockand the context for entropy decoding the secondary transform index canbe determined based on the intra prediction mode information for theblock.

In an example, the one of the intra prediction mode information for theblock, the size of the block, and the primary transform type used forthe block indicates the primary transform type used for the block andthe context for entropy decoding the secondary transform index can bedetermined based on the primary transform type used for the block.

At (S1930), the secondary transform index can be entropy decoded basedon the context that is determined at (S1920).

At (S1940), the secondary transform indicated by the secondary transformindex can be performed on the block. For example, the secondarytransform is an inverse secondary transform performed after an inverseprimary transform. In an example, the secondary transform is a LFNST. Inan example, the secondary transform is a non-separable secondarytransform. The process (1900) proceeds to (S1999), and terminates.

The process (1900) can be suitably adapted. Step(s) in the process(1900) can be modified and/or omitted. Additional step(s) can be added.Any suitable order of implementation can be used. For example, inaddition to the directional modes, the non-directional prediction modes,or the recursive filtering modes described with references to FIGS.9-11, the process (1900) is also applicable to other intra predictionmodes. In addition to the primary transform types described withreferences to FIGS. 15 and 16A-16D, the process (1900) is alsoapplicable to other suitable primary transform types or suitablecombinations of a horizontal primary transform type and a verticalprimary transform type.

Embodiments in the disclosure may be used separately or combined in anyorder. Further, each of the methods (or embodiments), an encoder, and adecoder may be implemented by processing circuitry (e.g., one or moreprocessors or one or more integrated circuits). In one example, the oneor more processors execute a program that is stored in a non-transitorycomputer-readable medium. Embodiments in the disclosure may be appliedto a luma block or a chroma block.

The techniques described above, can be implemented as computer softwareusing computer-readable instructions and physically stored in one ormore computer-readable media. For example, FIG. 20 shows a computersystem (2000) suitable for implementing certain embodiments of thedisclosed subject matter.

The computer software can be coded using any suitable machine code orcomputer language, that may be subject to assembly, compilation,linking, or like mechanisms to create code comprising instructions thatcan be executed directly, or through interpretation, micro-codeexecution, and the like, by one or more computer central processingunits (CPUs), Graphics Processing Units (GPUs), and the like.

The instructions can be executed on various types of computers orcomponents thereof, including, for example, personal computers, tabletcomputers, servers, smartphones, gaming devices, internet of thingsdevices, and the like.

The components shown in FIG. 20 for computer system (2000) are exemplaryin nature and are not intended to suggest any limitation as to the scopeof use or functionality of the computer software implementingembodiments of the present disclosure. Neither should the configurationof components be interpreted as having any dependency or requirementrelating to any one or combination of components illustrated in theexemplary embodiment of a computer system (2000).

Computer system (2000) may include certain human interface inputdevices. Such a human interface input device may be responsive to inputby one or more human users through, for example, tactile input (such as:keystrokes, swipes, data glove movements), audio input (such as: voice,clapping), visual input (such as: gestures), olfactory input (notdepicted). The human interface devices can also be used to capturecertain media not necessarily directly related to conscious input by ahuman, such as audio (such as: speech, music, ambient sound), images(such as: scanned images, photographic images obtain from a still imagecamera), video (such as two-dimensional video, three-dimensional videoincluding stereoscopic video).

Input human interface devices may include one or more of (only one ofeach depicted): keyboard (2001), mouse (2002), trackpad (2003), touchscreen (2010), data-glove (not shown), joystick (2005), microphone(2006), scanner (2007), camera (2008).

Computer system (2000) may also include certain human interface outputdevices. Such human interface output devices may be stimulating thesenses of one or more human users through, for example, tactile output,sound, light, and smell/taste. Such human interface output devices mayinclude tactile output devices (for example tactile feedback by thetouch-screen (2010), data-glove (not shown), or joystick (2005), butthere can also be tactile feedback devices that do not serve as inputdevices), audio output devices (such as: speakers (2009), headphones(not depicted)), visual output devices (such as screens (2010) toinclude CRT screens, LCD screens, plasma screens, OLED screens, eachwith or without touch-screen input capability, each with or withouttactile feedback capability—some of which may be capable to output twodimensional visual output or more than three dimensional output throughmeans such as stereographic output; virtual-reality glasses (notdepicted), holographic displays and smoke tanks (not depicted)), andprinters (not depicted).

Computer system (2000) can also include human accessible storage devicesand their associated media such as optical media including CD/DVD ROM/RW(2020) with CD/DVD or the like media (2021), thumb-drive (2022),removable hard drive or solid state drive (2023), legacy magnetic mediasuch as tape and floppy disc (not depicted), specialized ROM/ASIC/PLDbased devices such as security dongles (not depicted), and the like.

Those skilled in the art should also understand that term “computerreadable media” as used in connection with the presently disclosedsubject matter does not encompass transmission media, carrier waves, orother transitory signals.

Computer system (2000) can also include an interface (2054) to one ormore communication networks (2055). Networks can for example bewireless, wireline, optical. Networks can further be local, wide-area,metropolitan, vehicular and industrial, real-time, delay-tolerant, andso on. Examples of networks include local area networks such asEthernet, wireless LANs, cellular networks to include GSM, 3G, 4G, 5G,LTE and the like, TV wireline or wireless wide area digital networks toinclude cable TV, satellite TV, and terrestrial broadcast TV, vehicularand industrial to include CANBus, and so forth. Certain networkscommonly require external network interface adapters that attached tocertain general purpose data ports or peripheral buses (2049) (such as,for example USB ports of the computer system (2000)); others arecommonly integrated into the core of the computer system (2000) byattachment to a system bus as described below (for example Ethernetinterface into a PC computer system or cellular network interface into asmartphone computer system). Using any of these networks, computersystem (2000) can communicate with other entities. Such communicationcan be uni-directional, receive only (for example, broadcast TV),uni-directional send-only (for example CANbus to certain CANbusdevices), or bi-directional, for example to other computer systems usinglocal or wide area digital networks. Certain protocols and protocolstacks can be used on each of those networks and network interfaces asdescribed above.

Aforementioned human interface devices, human-accessible storagedevices, and network interfaces can be attached to a core (2040) of thecomputer system (2000).

The core (2040) can include one or more Central Processing Units (CPU)(2041), Graphics Processing Units (GPU) (2042), specialized programmableprocessing units in the form of Field Programmable Gate Areas (FPGA)(2043), hardware accelerators for certain tasks (2044), graphicsadapters (2050), and so forth. These devices, along with Read-onlymemory (ROM) (2045), Random-access memory (2046), internal mass storagesuch as internal non-user accessible hard drives, SSDs, and the like(2047), may be connected through a system bus (2048). In some computersystems, the system bus (2048) can be accessible in the form of one ormore physical plugs to enable extensions by additional CPUs, GPU, andthe like. The peripheral devices can be attached either directly to thecore's system bus (2048), or through a peripheral bus (2049). In anexample, the screen (2010) can be connected to the graphics adapter(2050). Architectures for a peripheral bus include PCI, USB, and thelike.

CPUs (2041), GPUs (2042), FPGAs (2043), and accelerators (2044) canexecute certain instructions that, in combination, can make up theaforementioned computer code. That computer code can be stored in ROM(2045) or RAM (2046). Transitional data can be also be stored in RAM(2046), whereas permanent data can be stored for example, in theinternal mass storage (2047). Fast storage and retrieve to any of thememory devices can be enabled through the use of cache memory, that canbe closely associated with one or more CPU (2041), GPU (2042), massstorage (2047), ROM (2045), RAM (2046), and the like.

The computer readable media can have computer code thereon forperforming various computer-implemented operations. The media andcomputer code can be those specially designed and constructed for thepurposes of the present disclosure, or they can be of the kind wellknown and available to those having skill in the computer software arts.

As an example and not by way of limitation, the computer system havingarchitecture (2000), and specifically the core (2040) can providefunctionality as a result of processor(s) (including CPUs, GPUs, FPGA,accelerators, and the like) executing software embodied in one or moretangible, computer-readable media. Such computer-readable media can bemedia associated with user-accessible mass storage as introduced above,as well as certain storage of the core (2040) that are of non-transitorynature, such as core-internal mass storage (2047) or ROM (2045). Thesoftware implementing various embodiments of the present disclosure canbe stored in such devices and executed by core (2040). Acomputer-readable medium can include one or more memory devices orchips, according to particular needs. The software can cause the core(2040) and specifically the processors therein (including CPU, GPU,FPGA, and the like) to execute particular processes or particular partsof particular processes described herein, including defining datastructures stored in RAM (2046) and modifying such data structuresaccording to the processes defined by the software. In addition or as analternative, the computer system can provide functionality as a resultof logic hardwired or otherwise embodied in a circuit (for example:accelerator (2044)), which can operate in place of or together withsoftware to execute particular processes or particular parts ofparticular processes described herein. Reference to software canencompass logic, and vice versa, where appropriate. Reference to acomputer-readable media can encompass a circuit (such as an integratedcircuit (IC)) storing software for execution, a circuit embodying logicfor execution, or both, where appropriate. The present disclosureencompasses any suitable combination of hardware and software.

APPENDIX A: ACRONYMS

-   JEM: joint exploration model-   VVC: versatile video coding-   BMS: benchmark set-   MV: Motion Vector-   HEVC: High Efficiency Video Coding-   SEI: Supplementary Enhancement Information-   VUI: Video Usability Information-   GOPs: Groups of Pictures-   TUs: Transform Units,-   PUs: Prediction Units-   CTUs: Coding Tree Units-   CTBs: Coding Tree Blocks-   PBs: Prediction Blocks-   HRD: Hypothetical Reference Decoder-   SNR: Signal Noise Ratio-   CPUs: Central Processing Units-   GPUs: Graphics Processing Units-   CRT: Cathode Ray Tube-   LCD: Liquid-Crystal Display-   OLED: Organic Light-Emitting Diode-   CD: Compact Disc-   DVD: Digital Video Disc-   ROM: Read-Only Memory-   RAM: Random Access Memory-   ASIC: Application-Specific Integrated Circuit-   PLD: Programmable Logic Device-   LAN: Local Area Network-   GSM: Global System for Mobile communications-   LTE: Long-Term Evolution-   CANBus: Controller Area Network Bus-   USB: Universal Serial Bus-   PCI: Peripheral Component Interconnect-   FPGA: Field Programmable Gate Areas-   SSD: solid-state drive-   IC: Integrated Circuit-   CU: Coding Unit

While this disclosure has described several exemplary embodiments, thereare alterations, permutations, and various substitute equivalents, whichfall within the scope of the disclosure. It will thus be appreciatedthat those skilled in the art will be able to devise numerous systemsand methods which, although not explicitly shown or described herein,embody the principles of the disclosure and are thus within the spiritand scope thereof.

What is claimed is:
 1. A method for video decoding in a decoder,comprising: decoding coded information for a transform block (TB) from acoded video bitstream, the coded information indicating one of intraprediction mode information for the TB, a size of the TB, and a primarytransform type used for the TB, the intra prediction mode informationfor the TB indicating an intra prediction mode used for the TB;determining a context for entropy decoding a secondary transform indexbased on the one of the intra prediction mode information for the TB,the size of the TB, and the primary transform type used for the TB, thesecondary transform index indicating a secondary transform in a set ofsecondary transforms that is to be performed on the TB; entropy decodingthe secondary transform index based on the context; and performing thesecondary transform indicated by the secondary transform index on theTB.
 2. The method of claim 1, wherein the one of the intra predictionmode information for the TB, the size of the TB, and the primarytransform type used for the TB indicates the size of the TB; and thedetermining the context includes determining the context for entropydecoding the secondary transform index based on the size of the TB. 3.The method of claim 2, wherein the size of the TB indicates a width W ofthe TB and a height H of the TB, a minimum of the width W of the TB andthe height H of the TB is L, and the determining the context furtherincludes determining the context based on L or L×L.
 4. The method ofclaim 1, wherein the one of the intra prediction mode information forthe TB, the size of the TB, and the primary transform type used for theTB indicates the intra prediction mode information for the TB; and thedetermining the context includes determining the context for entropydecoding the secondary transform index based on the intra predictionmode information for the TB.
 5. The method of claim 4, wherein the intraprediction mode information for the TB indicates a nominal mode index,the TB being predicted using a directional prediction mode that isdetermined based on the nominal mode index and an angular offset, andthe determining the context includes determining the context for entropydecoding the secondary transform index based on the nominal mode index.6. The method of claim 4, wherein the intra prediction mode informationfor the TB indicates a nominal mode index, the TB being predicted usinga directional prediction mode that is determined based on the nominalmode index and an angular offset, and the determining the contextincludes determining the context for entropy decoding the secondarytransform index based on an index value associated with the nominal modeindex.
 7. The method of claim 4, wherein the intra prediction modeinformation for the TB indicates a non-directional prediction modeindex, the TB being predicted using a non-directional prediction modeindicated by the non-directional prediction mode index, and thedetermining the context includes determining the context for entropydecoding the secondary transform index based on the non-directionalprediction mode index.
 8. The method of claim 4, wherein the intraprediction mode information for the TB indicates a recursive filteringmode used to predict the TB, the method includes determining a nominalmode index based on the recursive filtering mode, the nominal mode indexindicating a nominal mode, and the determining the context includesdetermining the context for entropy decoding the secondary transformindex based on the nominal mode index.
 9. The method of claim 1, whereinthe one of the intra prediction mode information for the TB, the size ofthe TB, and the primary transform type used for the TB indicates theprimary transform type used for the TB; and the determining the contextincludes determining the context for entropy decoding the secondarytransform index based on the primary transform type used for the TB. 10.The method of claim 9, wherein a primary transform indicated by theprimary transform type includes a horizontal transform indicated by ahorizontal primary transform type and a vertical transform indicated bya vertical primary transform type, and the determining the contextfurther includes determining the context for entropy decoding thesecondary transform index based on whether the horizontal primarytransform type and the vertical primary transform type are both discretecosine transforms (DCTs) or both asymmetric discrete sine transforms(ADSTs).
 11. The method of claim 9, wherein a primary transformindicated by the primary transform type includes a horizontal transformindicated by a horizontal primary transform type and a verticaltransform indicated by a vertical primary transform type, and thedetermining the context further includes determining the context forentropy decoding the secondary transform index based on whether thehorizontal primary transform type and the vertical primary transformtype are both discrete cosine transforms (DCTs) or both line graphtransforms (LGTs).
 12. The method of claim 9, wherein a primarytransform indicated by the primary transform type includes a horizontaltransform indicated by a horizontal primary transform type and avertical transform indicated by a vertical primary transform type, andthe determining the context further includes determining the context forentropy decoding the secondary transform index based on whether thehorizontal primary transform type and the vertical primary transformtype are (i) both discrete cosine transforms (DCTs), (ii) both linegraph transforms (LGTs), (iii) a DCT and an LGT, respectively, or (iv)an LGT and a DCT, respectively.
 13. The method of claim 9, wherein aprimary transform indicated by the primary transform type includes ahorizontal transform indicated by a horizontal primary transform typeand a vertical transform indicated by a vertical primary transform type,and the determining the context further includes determining the contextfor entropy decoding the secondary transform index based on whether thehorizontal primary transform type and the vertical primary transformtype are (i) both discrete cosine transforms (DCTs), (ii) both linegraph transforms (LGTs), (iii) a DCT and an identity transform (IDTX),respectively, or (iv) an IDTX and a DCT, respectively.
 14. An apparatusfor video decoding, comprising processing circuitry configured to:decode coded information for a transform block (TB) from a coded videobitstream, the coded information indicating one of intra prediction modeinformation for the TB, a size of the TB, and a primary transform typeused for the TB, the intra prediction mode information for the TBindicating an intra prediction mode used for the TB; determine a contextfor entropy decoding a secondary transform index based on the one of theintra prediction mode information for the TB, the size of the TB, andthe primary transform type used for the TB, the secondary transformindex indicating a secondary transform in a set of secondary transformsthat is to be performed on the TB; entropy decode the secondarytransform index based on the context; and perform the secondarytransform indicated by the secondary transform index on the TB.
 15. Theapparatus of claim 14, wherein the one of the intra prediction modeinformation for the TB, the size of the TB, and the primary transformtype used for the TB indicates the size of the TB; and the processingcircuitry is configured to determine the context for entropy decodingthe secondary transform index based on the size of the TB.
 16. Theapparatus of claim 14, wherein the one of the intra prediction modeinformation for the TB, the size of the TB, and the primary transformtype used for the TB indicates the intra prediction mode information forthe TB; and the processing circuitry is configured to determine thecontext for entropy decoding the secondary transform index based on theintra prediction mode information for the TB.
 17. The apparatus of claim14, wherein the one of the intra prediction mode information for the TB,the size of the TB, and the primary transform type used for the TBindicates the primary transform type used for the TB; and the processingcircuitry is configured to determine the context for entropy decodingthe secondary transform index based on the primary transform type usedfor the TB.
 18. The apparatus of claim 17, wherein a primary transformindicated by the primary transform type includes a horizontal transformindicated by a horizontal primary transform type and a verticaltransform indicated by a vertical primary transform type; and theprocessing circuitry is configured to determine the context for entropydecoding the secondary transform index based on whether the horizontalprimary transform type and the vertical primary transform type are bothdiscrete cosine transforms (DCTs) or both asymmetric discrete sinetransforms (ADSTs).
 19. The apparatus of claim 17, wherein a primarytransform indicated by the primary transform type includes a horizontaltransform indicated by a horizontal primary transform type and avertical transform indicated by a vertical primary transform type; andthe processing circuitry is configured to determine the context forentropy decoding the secondary transform index based on whether thehorizontal primary transform type and the vertical primary transformtype are both discrete cosine transforms (DCTs) or both line graphtransforms (LGTs).
 20. The apparatus of claim 17, wherein a primarytransform indicated by the primary transform type includes a horizontaltransform indicated by a horizontal primary transform type and avertical transform indicated by a vertical primary transform type; andthe processing circuitry is configured to determine the context forentropy decoding the secondary transform index based on whether thehorizontal primary transform type and the vertical primary transformtype are (i) both discrete cosine transforms (DCTs), (ii) both linegraph transforms (LGTs), (iii) a DCT and an LGT, respectively, or (iv)an LGT and a DCT, respectively.